1 Context

1.1 Overall Factor Analysis Steps

  1. Are the data suitable for factor analysis?
    • Bartlett’s Sphericity Test Tests whether correlations are different than zero across all the data. If they are close to zero, there owuld be no common factors to find
    • Kaiser-Meyer-Olkin Criterion Test sampling adequacy, measures the degree to wich each variable predicts all other variables in the data set.
  2. Imputation of Missing Variables
    • Generate categorical values for missing data using Multiple Correspondence Analysis/Missing Fuzzy Average Method
  3. Calculate between-item Correlations
    • the polychoric (for orderd categorical variables) and regular Pearson correlation are calculated for later use in factor analysis and for checking other aspects of the factor analysis. The polychoric correlation is the input to the actual factor analysis.
  4. Estimate Number of Factors
    • Parallel analysis
    • Minimim Average Partial (MAP)
  5. Run factor analysis for a range of possible number of factors
    • produces
      • measures of model fit
      • communalities (how much each item covaries with the other items)
      • loadings (correlation between item and factor(s))
  6. Evaluate Reliability of Model..
    • alpha
    • omega
  7. Select best model (number of factors) given model fit statistics and judgement based on understanding of behavior.

1.2 Context Text Description

All data were used in the factorAnalysis1.1.html document you already received.

A series of factoro analyses were run on all items in the file factorAnalysis1.1.html. THe literature suggests doing this so you can compare both statistical measures of how well it fits, and also how logical the grouping of factors is according to knowledge of the subject.

This set of analyses showed that some items had really low communalities, meaning that they didn’t covary much with any of the other items. This means they will not be robust parts of any factor, and they recommend that you remove these from the analysis.

Models with different numbers of factors had different numbers of items with communalities less than 0.4. So a new data set was made for each number of factors, with only the items with communalities of 0.4 or larger.

Because each number of factors require a different data set (different numbers of items), all the steps had to be rerun sstarting with imputation. Those are the models included in this document.

2 Factor Analyses

Testing analyses from 11 - 18 factors.

2.1 11 Factors

2.1.1 Imputation of Missing Items (11 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.1.2 11-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.1.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum11, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1906 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 2211 DF, p = NaN.

2.1.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570731

2.1.3 11-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.1.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF11, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1904 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 2211 DF, p = NaN.

2.1.3.2 11-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570731

2.1.4 Between-Item Correlations

2.1.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.889.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.69. The maximum correlation was 0.887.

2.1.5 Estimating Number of Factors

2.1.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF11, n.obs = nrow(imputedNumericDF11), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 14.

2.1.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
Number of Factors MAP value
1 0.0251
2 0.0208
3 0.0163
4 0.0147
5 0.0142
6 0.0133
7 0.0126
8 0.0121
9 0.0118
10 0.0117
11 0.0115
12 0.0113
13 0.0113
14 0.0117
15 0.0117
16 0.0120
17 0.0121
18 0.0126

2.1.6 Factor Analysis for 11 Factors

2.1.6.1 11 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1904 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 5.742761^{4}
  • degrees of freedom: 1529
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.1162773. Should be > 0.9; need reference)

2.1.6.2 11 Factor Model Communalities

fanal11.communality
TRAIN01 0.44
TRAIN02 0.24
TRAIN04 0.61
TRAIN05 0.32
TRAIN06 0.25
TRAIN07 0.60
TRAIN08 0.61
AGG09 0.76
AGG10 0.63
AGG11 0.76
AGG12 0.79
AGG13 0.95
AGG14 0.45
AGG15 0.76
AGG16 0.73
AGG17 0.55
AGG18 0.72
AGG19 0.59
AGG20 0.47
FEAR21 0.81
FEAR22 0.32
FEAR23 0.78
FEAR24 0.84
FEAR25 0.46
FEAR27 0.67
FEAR28 0.64
FEAR29 0.13
FEAR31 0.59
SEPR32 0.69
SEPR33 0.53
SEPR34 0.73
EXCITE35 0.48
EXCITE36 0.63
EXCITE37 0.58
EXCITE38 0.62
ATT39 0.30
ATT40 0.28
ATT41 0.32
ATT42 0.35
PLAY43 0.55
PLAY44 0.79
PLAY45 0.74
PLAY46 0.71
IMP47 0.46
IMP48 0.41
IMP49 0.39
MISC50 0.32
MISC51 0.37
MISC52 0.23
MISC54 0.58
MISC55 0.70
MISC56 0.53
MISC57 0.33
MISC58 0.23
MISC59 0.54
MISC60 0.38
MISC61 0.50
MISC62 0.48
MISC63 0.37
MISC64 0.54
MISC65 0.60
MISC66 0.69
MISC67 0.62
MISC68 0.20
MISC69 0.22
MISC70 0.33
MISC71 0.28

2.1.6.3 How many communalities < 0.40?

There are 21 items with communality < 0.40.

fanal11.communality item
TRAIN02 0.24 TRAIN02
TRAIN05 0.32 TRAIN05
TRAIN06 0.25 TRAIN06
FEAR22 0.32 FEAR22
FEAR29 0.13 FEAR29
ATT39 0.30 ATT39
ATT40 0.28 ATT40
ATT41 0.32 ATT41
ATT42 0.35 ATT42
IMP49 0.39 IMP49
MISC50 0.32 MISC50
MISC51 0.37 MISC51
MISC52 0.23 MISC52
MISC57 0.33 MISC57
MISC58 0.23 MISC58
MISC60 0.38 MISC60
MISC63 0.37 MISC63
MISC68 0.20 MISC68
MISC69 0.22 MISC69
MISC70 0.33 MISC70
MISC71 0.28 MISC71

2.1.6.4 11 Factor Model Loadings

PA2 PA10 PA1 PA5 PA11 PA6 PA8 PA3 PA4 PA7 PA9
TRAIN01 -0.14 -0.12 0.17 -0.02 -0.09 0.06 0.04 0.05 0.54 -0.02 -0.01
TRAIN02 -0.04 0.06 0.14 -0.02 0.00 0.03 0.01 -0.03 0.40 0.09 -0.05
TRAIN04 -0.04 0.05 0.30 0.01 -0.02 0.05 -0.04 -0.04 0.63 0.02 -0.08
TRAIN05 0.04 -0.15 0.12 0.14 -0.06 0.00 -0.02 0.13 0.43 0.07 0.02
TRAIN06 -0.09 0.02 0.21 -0.04 0.10 0.07 0.06 -0.12 0.29 -0.03 -0.13
TRAIN07 -0.13 0.02 0.60 -0.02 -0.03 0.05 0.03 -0.07 0.27 0.00 -0.06
TRAIN08 -0.74 0.01 0.08 0.01 0.06 0.01 -0.05 -0.03 0.06 0.05 0.03
AGG09 0.05 0.29 0.07 0.06 0.03 -0.06 0.08 0.71 0.03 -0.05 0.04
AGG10 0.03 0.05 -0.04 0.06 -0.03 0.06 0.18 0.68 -0.04 0.01 -0.01
AGG11 -0.09 -0.02 -0.13 0.81 0.00 0.12 0.04 0.01 0.09 -0.12 0.07
AGG12 -0.04 0.08 0.06 0.88 0.01 -0.03 -0.01 -0.04 -0.07 0.04 -0.03
AGG13 -0.01 0.03 0.02 0.95 0.01 -0.10 -0.02 0.07 0.03 0.05 0.01
AGG14 -0.09 0.05 -0.03 -0.07 0.05 0.08 0.16 0.59 -0.01 0.06 0.09
AGG15 -0.02 0.26 0.00 0.13 0.01 -0.03 0.06 0.70 0.01 -0.02 -0.04
AGG16 0.00 -0.04 0.09 0.02 0.02 -0.03 0.75 0.25 -0.01 0.00 -0.05
AGG17 0.10 0.08 -0.01 0.17 0.21 0.22 0.08 0.36 0.08 0.11 -0.34
AGG18 0.06 -0.08 0.05 0.03 -0.03 0.02 0.75 0.27 -0.02 -0.03 0.02
AGG19 0.15 -0.11 0.06 0.30 0.02 0.13 0.57 0.10 -0.06 0.10 -0.13
AGG20 0.02 -0.13 0.01 0.48 0.02 0.12 0.41 -0.07 -0.07 0.02 -0.04
FEAR21 0.01 0.83 0.03 0.07 0.02 0.06 -0.04 0.13 0.00 0.01 -0.04
FEAR22 -0.04 0.25 0.23 0.06 0.24 0.08 0.05 -0.21 -0.10 0.05 -0.04
FEAR23 0.00 0.79 0.01 0.00 0.06 0.05 0.01 0.18 -0.01 -0.02 0.02
FEAR24 -0.08 0.83 0.03 0.06 -0.01 0.00 0.00 0.15 -0.05 0.03 0.00
FEAR25 0.02 0.28 0.21 0.13 0.35 0.03 0.02 -0.08 0.05 0.02 0.06
FEAR27 -0.04 0.45 -0.10 -0.03 0.10 -0.04 0.59 -0.18 0.11 -0.03 0.10
FEAR28 0.06 0.49 0.20 0.06 0.38 0.06 -0.02 -0.09 -0.03 0.06 -0.09
FEAR29 -0.07 0.12 0.05 0.11 0.08 0.08 0.11 -0.04 0.08 0.08 -0.02
FEAR31 -0.07 0.42 -0.04 -0.04 0.12 -0.02 0.52 -0.29 0.11 -0.01 0.09
SEPR32 0.00 0.12 0.06 -0.02 -0.07 0.81 0.05 -0.04 -0.10 0.08 -0.06
SEPR33 -0.01 -0.01 0.08 0.05 -0.01 0.69 0.00 -0.08 -0.02 0.03 0.04
SEPR34 -0.03 -0.05 -0.07 -0.06 0.11 0.82 -0.04 0.06 0.12 -0.03 0.04
EXCITE35 -0.11 0.09 0.04 -0.11 -0.10 0.16 0.01 0.02 -0.05 0.64 0.06
EXCITE36 0.20 -0.01 0.05 0.00 0.02 -0.05 -0.08 0.03 -0.01 0.73 -0.04
EXCITE37 -0.07 -0.01 -0.05 0.02 -0.02 0.03 0.03 -0.01 0.04 0.77 -0.02
EXCITE38 0.03 -0.02 -0.14 0.05 0.09 -0.04 0.01 -0.05 0.06 0.76 0.00
ATT39 -0.06 0.09 0.14 -0.13 -0.11 0.08 0.03 0.09 -0.38 0.23 0.22
ATT40 -0.20 0.07 0.29 -0.03 0.08 0.13 0.03 0.05 -0.15 0.11 0.14
ATT41 -0.06 -0.02 0.13 0.08 -0.02 0.11 0.02 -0.07 -0.21 0.12 0.45
ATT42 -0.12 -0.02 0.09 0.02 0.07 0.13 0.10 -0.01 -0.04 0.16 0.43
PLAY43 0.52 -0.25 -0.02 -0.04 0.05 -0.09 0.00 -0.30 -0.02 0.06 0.12
PLAY44 0.88 0.00 0.03 -0.01 -0.01 0.00 0.08 -0.05 0.02 0.06 -0.02
PLAY45 0.82 0.06 -0.01 -0.09 -0.03 -0.06 0.02 0.00 -0.05 0.01 0.06
PLAY46 0.77 -0.04 -0.14 -0.02 0.03 0.05 -0.06 0.09 0.07 0.04 -0.08
IMP47 0.21 0.09 -0.06 0.02 -0.01 0.04 0.05 0.00 0.43 0.17 0.29
IMP48 0.15 0.04 0.04 0.20 0.00 0.05 0.05 -0.05 0.28 0.13 0.32
IMP49 0.00 0.05 0.05 0.20 -0.02 -0.06 0.01 0.00 0.44 0.16 0.16
MISC50 0.04 0.00 -0.02 0.21 0.09 0.24 -0.06 0.02 0.20 0.08 0.21
MISC51 -0.13 -0.16 -0.01 0.02 0.02 0.28 0.01 0.11 0.35 0.05 0.17
MISC52 -0.32 -0.04 0.00 0.06 0.05 -0.07 0.05 0.00 0.05 0.11 0.34
MISC54 -0.11 0.02 0.16 -0.01 0.67 -0.02 0.02 -0.04 0.00 0.08 -0.02
MISC55 0.02 -0.03 -0.04 -0.06 0.87 0.02 0.01 0.04 -0.07 0.00 0.00
MISC56 -0.03 -0.03 0.03 0.11 0.71 -0.03 -0.04 0.01 0.01 -0.04 0.03
MISC57 0.06 -0.06 0.10 0.14 -0.05 0.16 -0.01 -0.05 0.24 0.10 0.26
MISC58 0.13 -0.03 0.05 0.33 0.01 0.26 -0.04 0.00 0.04 -0.12 0.11
MISC59 0.27 0.05 0.14 0.10 -0.02 0.37 -0.08 -0.04 0.13 -0.01 0.37
MISC60 0.30 0.02 0.07 -0.04 -0.03 0.06 -0.14 0.01 -0.01 0.14 0.41
MISC61 0.42 0.01 0.04 -0.02 -0.12 0.17 -0.13 0.11 -0.06 0.16 0.30
MISC62 0.00 -0.03 0.40 -0.04 -0.01 -0.06 0.41 0.04 0.09 0.04 0.22
MISC63 -0.01 -0.02 0.35 0.04 0.11 -0.14 0.08 0.05 0.09 0.14 0.31
MISC64 -0.07 -0.14 0.66 0.00 0.06 0.05 0.02 0.07 0.08 -0.04 0.00
MISC65 -0.09 -0.12 0.62 -0.03 0.05 0.05 0.14 0.04 0.15 -0.04 0.09
MISC66 -0.05 0.21 0.63 -0.01 0.18 0.05 -0.06 0.00 0.07 -0.06 0.02
MISC67 -0.07 0.20 0.62 0.07 0.11 0.07 -0.01 -0.03 -0.06 -0.06 0.05
MISC68 0.02 -0.12 -0.09 0.11 0.31 0.07 0.00 0.12 0.19 0.05 0.08
MISC69 -0.06 -0.05 -0.07 -0.01 0.33 0.10 0.03 0.11 0.14 0.03 0.20
MISC70 0.02 -0.06 -0.05 0.07 0.08 0.14 0.08 0.19 0.08 0.00 0.43
MISC71 -0.03 -0.04 0.08 -0.05 0.26 0.10 -0.07 0.08 0.05 -0.06 0.38
2.1.6.4.1 11 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
14 PA1 0.29 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
45 PA1 0.35 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
46 PA1 0.66 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
47 PA1 0.62 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
48 PA1 0.63 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
49 PA1 0.62 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
66 PA1 0.60 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
67 PA1 0.08 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
21 PA10 0.83 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
22 PA10 0.25 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
23 PA10 0.79 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
24 PA10 0.83 FEAR24 When an unfamiliar person tries to touch or pet the dog
27 PA10 0.49 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
28 PA10 0.12 FEAR29 When having nails trimmed, or feet touched/handled
25 PA11 0.35 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
36 PA11 0.67 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
37 PA11 0.87 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
38 PA11 0.71 MISC56 Nervous or frightened when ascending or descending some types of stairs
50 PA11 0.31 MISC68 Chases own tail/hind end
51 PA11 0.33 MISC69 Chases/follows shadows, light spots, etc.
43 PA2 0.42 MISC61 Active, energetic, always on the go
54 PA2 0.52 PLAY43 Eagerly engages in play with new/unfamiliar people
55 PA2 0.88 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
56 PA2 0.82 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
57 PA2 0.77 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.71 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.68 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.59 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.70 AGG15 When an unfamiliar person tries to touch or pet the dog
9 PA3 0.36 AGG17 When stared at directly by you or another familiar person
30 PA4 0.43 IMP47 Impulsive; doesn’t seem to think before s/he acts
32 PA4 0.44 IMP49 Is difficult to interrupt or distract when doing things s/he wants to do
34 PA4 0.35 MISC51 Escapes or would escape from home, yard or kennel given the chance
61 PA4 0.54 TRAIN01 Is hard to recall when off the leash
62 PA4 0.40 TRAIN02 Is slow to obey a ‘sit’ command
63 PA4 0.63 TRAIN04 Has difficulty attending/listening to things you say or do
64 PA4 0.43 TRAIN05 Is slow to respond to corrections or reprimands: thick-skinned
65 PA4 0.29 TRAIN06 Is slow to learn new tricks or tasks
3 PA5 0.81 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA5 0.88 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA5 0.95 AGG13 When his/her food is taken away by you or another familiar person
12 PA5 0.48 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
40 PA5 0.33 MISC58 Urinates against objects/furnishings indoors
33 PA6 0.24 MISC50 NA
41 PA6 0.37 MISC59 Hyperactive, restless, has trouble settling down
58 PA6 0.81 SEPR32 Restlessness/agitation/pacing when left alone
59 PA6 0.69 SEPR33 Barking or whining when left alone
60 PA6 0.82 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
13 PA7 0.23 ATT39 Displays a strong attachment for you or another familiar person
17 PA7 0.64 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
18 PA7 0.73 EXCITE36 Excitable when playing with you or other familiar persons
19 PA7 0.77 EXCITE37 Excitable just before being taken out for a walk
20 PA7 0.76 EXCITE38 Excitable just before being taken out for work or training
8 PA8 0.75 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA8 0.75 AGG18 When barked, growled, or lunged at by another dog
11 PA8 0.57 AGG19 Towards other familiar dogs
26 PA8 0.59 FEAR27 When approached directly by an unfamiliar dog
29 PA8 0.52 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
44 PA8 0.41 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
15 PA9 0.45 ATT41 Tends to nudge or paw you (or others) for attention
16 PA9 0.43 ATT42 Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
31 PA9 0.32 IMP48 Becomes frustrated/impatient in a wide range of situations
35 PA9 0.34 MISC52 Begs persistently for food when people are eating
39 PA9 0.26 MISC57 Pulls excessively hard when on leash
42 PA9 0.41 MISC60 Playful, puppyish, boisterous
52 PA9 0.43 MISC70 Barks persistently when alarmed or excited
53 PA9 0.38 MISC71 Licks people or objects excessively

2.1.7 11 Model Reliability Measures

2.2 12 Factors

2.2.1 Imputation of Missing Items (12 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.2.2 12-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.2.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum12, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1232 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1378 DF, p = NaN.

2.2.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8457672

2.2.3 12-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.2.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF12, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1232 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1378 DF, p = NaN.

2.2.3.2 12-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8457672

2.2.4 Between-Item Correlations

2.2.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.9.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.692. The maximum correlation was 0.904.

2.2.5 Estimating Number of Factors

2.2.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF12, n.obs = nrow(imputedNumericDF12), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 12.

2.2.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
Number of Factors MAP value
1 0.0326
2 0.0279
3 0.0219
4 0.0203
5 0.0193
6 0.0178
7 0.0174
8 0.0163
9 0.0156
10 0.0149
11 0.0153
12 0.0151
13 0.0157
14 0.0163
15 0.0170
16 0.0176
17 0.0181
18 0.0189

2.2.6 Factor Analysis for 12 Factors

2.2.6.1 12 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1232 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 5.1891719^{4}
  • degrees of freedom: 808
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.0349984. Should be > 0.9; need reference)

2.2.6.2 12 Factor Model Communalities

fanal12.communality
TRAIN01 0.47
TRAIN03 0.41
TRAIN04 0.58
TRAIN07 0.63
TRAIN08 0.62
AGG09 0.75
AGG10 0.67
AGG11 0.76
AGG12 0.76
AGG13 1.00
AGG14 0.50
AGG15 0.79
AGG16 0.78
AGG17 0.62
AGG18 0.75
AGG19 0.60
AGG20 0.45
FEAR21 0.82
FEAR23 0.79
FEAR24 0.86
FEAR25 0.43
FEAR26 0.35
FEAR27 0.68
FEAR28 0.65
FEAR30 0.31
FEAR31 0.58
SEPR32 0.69
SEPR33 0.60
SEPR34 0.68
EXCITE35 0.48
EXCITE36 0.61
EXCITE37 0.61
EXCITE38 0.64
PLAY43 0.56
PLAY44 0.81
PLAY45 0.77
PLAY46 0.71
IMP47 0.45
IMP48 0.41
MISC52 0.53
MISC53 0.52
MISC54 0.64
MISC55 0.72
MISC56 0.62
MISC59 0.50
MISC60 0.53
MISC61 0.68
MISC62 0.45
MISC64 0.64
MISC65 0.64
MISC66 0.68
MISC67 0.58
MISC68 0.14

2.2.6.3 How many communalities < 0.40?

There are 3 items with communality < 0.40.

fanal12.communality item
FEAR26 0.35 FEAR26
FEAR30 0.31 FEAR30
MISC68 0.14 MISC68

2.2.6.4 12 Factor Model Loadings

PA1 PA2 PA4 PA12 PA5 PA9 PA6 PA8 PA7 PA3 PA11 PA10
TRAIN01 -0.09 -0.06 -0.02 0.13 0.05 -0.07 0.02 0.01 -0.04 0.60 -0.07 0.06
TRAIN03 -0.01 -0.09 -0.08 -0.04 0.07 0.06 -0.02 0.07 0.09 0.59 0.03 0.04
TRAIN04 0.07 -0.03 0.03 0.26 -0.01 -0.02 -0.06 -0.01 0.02 0.63 -0.02 -0.01
TRAIN07 0.05 -0.11 0.01 0.61 0.01 -0.05 -0.09 0.02 0.01 0.29 -0.02 -0.05
TRAIN08 0.03 -0.70 0.02 0.12 -0.04 0.07 -0.04 0.00 0.04 0.05 -0.03 0.08
AGG09 0.29 0.03 0.06 0.03 0.15 0.06 0.65 -0.07 -0.07 0.07 0.09 -0.04
AGG10 0.01 0.09 0.06 0.01 0.17 -0.04 0.71 0.10 -0.01 -0.08 -0.06 0.07
AGG11 0.00 -0.07 0.81 -0.14 0.07 -0.01 -0.03 0.10 -0.11 0.15 0.01 0.02
AGG12 0.05 -0.09 0.86 0.04 0.00 0.02 -0.02 0.00 0.05 -0.10 0.01 0.00
AGG13 0.03 0.03 0.99 0.07 -0.03 -0.01 0.06 -0.07 0.04 -0.03 0.00 0.04
AGG14 0.03 0.01 -0.08 0.08 0.13 -0.02 0.62 0.11 0.06 -0.07 -0.09 0.14
AGG15 0.27 -0.03 0.12 -0.02 0.10 0.02 0.70 -0.03 -0.02 0.02 0.03 0.01
AGG16 -0.02 -0.06 -0.01 0.02 0.82 0.06 0.18 -0.05 0.00 0.04 0.00 -0.06
AGG17 0.07 0.22 0.21 0.13 0.02 0.09 0.34 0.19 0.15 0.01 -0.40 -0.20
AGG18 -0.06 0.01 0.02 -0.01 0.81 0.00 0.19 0.01 -0.04 0.05 0.02 -0.02
AGG19 -0.08 0.06 0.27 -0.03 0.62 0.04 0.04 0.09 0.12 0.03 -0.03 -0.15
AGG20 -0.11 0.03 0.44 -0.06 0.39 0.03 -0.06 0.11 0.02 0.03 -0.10 0.01
FEAR21 0.86 -0.01 0.07 -0.03 -0.05 0.03 0.11 0.03 0.00 0.03 0.01 -0.04
FEAR23 0.81 -0.03 0.00 0.00 0.01 0.05 0.14 0.05 -0.01 -0.02 0.03 -0.06
FEAR24 0.87 -0.10 0.06 -0.01 -0.01 -0.03 0.11 -0.01 0.04 -0.03 0.01 -0.02
FEAR25 0.32 0.05 0.09 0.18 0.00 0.30 -0.09 0.05 0.04 0.11 -0.07 0.01
FEAR26 0.45 0.09 0.14 0.01 0.03 0.05 -0.01 0.13 0.00 0.03 -0.09 0.12
FEAR27 0.45 0.05 -0.01 0.08 0.51 0.02 -0.21 -0.01 -0.01 -0.11 -0.10 0.22
FEAR28 0.53 0.07 0.03 0.11 -0.06 0.38 -0.10 0.07 0.06 0.05 -0.11 -0.05
FEAR30 0.14 0.11 0.17 0.06 0.05 0.18 -0.08 0.20 -0.01 0.04 -0.17 0.17
FEAR31 0.40 0.04 -0.04 0.11 0.41 0.06 -0.28 0.01 0.00 -0.08 -0.13 0.26
SEPR32 0.10 -0.05 -0.05 0.00 0.03 -0.05 0.00 0.82 0.07 -0.05 0.01 -0.05
SEPR33 -0.04 -0.03 0.05 0.06 -0.02 0.00 -0.06 0.76 -0.02 -0.03 0.07 0.03
SEPR34 -0.06 0.00 -0.04 0.00 -0.05 0.06 0.06 0.81 -0.04 0.07 -0.01 0.03
EXCITE35 0.10 -0.15 -0.11 0.02 0.03 -0.08 0.02 0.14 0.63 -0.01 0.12 0.02
EXCITE36 0.00 0.16 0.03 0.05 -0.07 0.03 0.02 -0.05 0.70 -0.03 0.08 -0.04
EXCITE37 -0.02 -0.08 0.01 -0.01 0.03 -0.03 0.00 0.01 0.80 0.01 0.01 0.02
EXCITE38 -0.02 0.05 0.04 -0.11 0.00 0.06 -0.05 -0.03 0.77 0.05 -0.04 0.04
PLAY43 -0.26 0.50 -0.02 0.03 -0.03 0.01 -0.28 -0.07 0.07 -0.09 0.11 0.07
PLAY44 0.00 0.85 0.00 0.00 0.06 -0.03 -0.05 -0.01 0.05 0.03 0.05 -0.09
PLAY45 0.03 0.83 -0.09 0.01 -0.03 -0.04 0.05 -0.05 0.00 -0.10 0.07 0.05
PLAY46 -0.06 0.77 -0.02 -0.14 -0.08 0.00 0.12 0.03 0.03 0.06 -0.01 -0.05
IMP47 0.08 0.30 0.02 -0.03 0.04 0.01 0.02 0.05 0.12 0.38 0.14 0.29
IMP48 0.03 0.22 0.17 0.05 0.05 0.02 -0.02 0.10 0.11 0.25 0.15 0.29
MISC52 -0.08 -0.13 0.01 0.04 -0.08 0.06 0.17 -0.01 0.07 -0.01 -0.03 0.70
MISC53 -0.13 -0.08 0.17 -0.05 -0.11 -0.02 0.04 0.07 0.01 0.13 0.02 0.63
MISC54 0.01 -0.04 -0.04 0.13 -0.01 0.71 -0.01 -0.01 0.07 0.01 -0.12 0.09
MISC55 -0.03 -0.02 -0.07 -0.07 0.06 0.88 0.01 0.03 0.00 -0.03 0.03 -0.06
MISC56 -0.05 -0.05 0.11 0.00 -0.01 0.78 0.01 -0.04 -0.05 0.00 0.08 0.05
MISC59 0.06 0.17 0.07 0.09 0.00 0.03 -0.04 0.35 0.00 0.16 0.37 0.13
MISC60 0.03 0.11 0.00 0.05 0.00 0.07 -0.04 0.03 0.11 0.02 0.65 0.02
MISC61 0.01 0.18 0.03 0.01 0.02 -0.04 0.06 0.14 0.15 -0.06 0.66 -0.09
MISC62 0.01 -0.04 -0.03 0.40 0.43 0.00 -0.02 -0.02 0.04 0.03 0.17 0.10
MISC64 -0.15 -0.03 0.06 0.80 -0.03 0.00 0.08 0.05 -0.03 -0.02 -0.02 -0.03
MISC65 -0.09 -0.05 -0.03 0.69 0.11 0.00 0.03 0.05 -0.01 0.13 -0.01 0.08
MISC66 0.23 -0.05 -0.02 0.58 -0.08 0.20 0.00 0.05 -0.06 0.10 0.02 0.02
MISC67 0.20 -0.13 0.04 0.55 -0.01 0.15 0.00 0.06 -0.05 -0.03 0.08 0.03
MISC68 -0.08 0.08 0.21 0.09 0.02 0.17 0.02 0.06 0.05 0.08 0.03 -0.06
2.2.6.4.1 12 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
17 PA1 0.86 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
18 PA1 0.81 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
19 PA1 0.87 FEAR24 When an unfamiliar person tries to touch or pet the dog
20 PA1 0.32 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
21 PA1 0.45 FEAR26 When examined/treated by a veterinarian
23 PA1 0.53 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
27 PA10 0.29 IMP48 Becomes frustrated/impatient in a wide range of situations
28 PA10 0.70 MISC52 Begs persistently for food when people are eating
29 PA10 0.63 MISC53 Steals food
33 PA11 0.37 MISC59 Hyperactive, restless, has trouble settling down
34 PA11 0.65 MISC60 Playful, puppyish, boisterous
35 PA11 0.66 MISC61 Active, energetic, always on the go
37 PA12 0.80 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
38 PA12 0.69 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
39 PA12 0.58 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
40 PA12 0.55 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
52 PA12 0.61 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
53 PA12 0.12 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
42 PA2 0.50 PLAY43 Eagerly engages in play with new/unfamiliar people
43 PA2 0.85 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
44 PA2 0.83 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
45 PA2 0.77 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
26 PA3 0.38 IMP47 Impulsive; doesn’t seem to think before s/he acts
49 PA3 0.60 TRAIN01 Is hard to recall when off the leash
50 PA3 0.59 TRAIN03 Is slow to obey a ‘stay’ command
51 PA3 0.63 TRAIN04 Has difficulty attending/listening to things you say or do
3 PA4 0.81 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.86 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.99 AGG13 When his/her food is taken away by you or another familiar person
12 PA4 0.44 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
41 PA4 0.21 MISC68 Chases own tail/hind end
8 PA5 0.82 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA5 0.81 AGG18 When barked, growled, or lunged at by another dog
11 PA5 0.62 AGG19 Towards other familiar dogs
22 PA5 0.51 FEAR27 When approached directly by an unfamiliar dog
25 PA5 0.41 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
36 PA5 0.43 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
1 PA6 0.65 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA6 0.71 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA6 0.62 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA6 0.70 AGG15 When an unfamiliar person tries to touch or pet the dog
9 PA6 0.34 AGG17 When stared at directly by you or another familiar person
13 PA7 0.63 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
14 PA7 0.70 EXCITE36 Excitable when playing with you or other familiar persons
15 PA7 0.80 EXCITE37 Excitable just before being taken out for a walk
16 PA7 0.77 EXCITE38 Excitable just before being taken out for work or training
24 PA8 0.20 FEAR30 When groomed or bathed
46 PA8 0.82 SEPR32 Restlessness/agitation/pacing when left alone
47 PA8 0.76 SEPR33 Barking or whining when left alone
48 PA8 0.81 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
30 PA9 0.71 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
31 PA9 0.88 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
32 PA9 0.78 MISC56 Nervous or frightened when ascending or descending some types of stairs

2.2.7 12 Model Reliability Measures

2.3 13 Factors

2.3.1 Imputation of Missing Items (13 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.3.2 13-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.3.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum13, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1242 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1378 DF, p = NaN.

2.3.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8463937

2.3.3 13-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.3.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF13, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1242 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1378 DF, p = NaN.

2.3.3.2 13-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8463937

2.3.4 Between-Item Correlations

2.3.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.899.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.692. The maximum correlation was 0.903.

2.3.5 Estimating Number of Factors

2.3.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF13, n.obs = nrow(imputedNumericDF13), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 12.

2.3.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully
Number of Factors MAP value
1 0.0317
2 0.0273
3 0.0220
4 0.0203
5 0.0192
6 0.0178
7 0.0173
8 0.0174
9 0.0157
10 0.0150
11 0.0152
12 0.0151
13 0.0156
14 0.0167
15 0.0173
16 0.0176
17 0.0180
18 0.0189

2.3.6 Factor Analysis for 13 Factors

2.3.6.1 13 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1242 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 5.0849884^{4}
  • degrees of freedom: 767
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.0736639. Should be > 0.9; need reference)

2.3.6.2 13 Factor Model Communalities

fanal13.communality
TRAIN01 0.51
TRAIN03 0.40
TRAIN04 0.59
TRAIN07 0.63
TRAIN08 0.62
AGG09 0.73
AGG10 0.68
AGG11 0.76
AGG12 0.80
AGG13 1.00
AGG14 0.49
AGG15 0.78
AGG16 0.78
AGG17 0.67
AGG18 0.74
AGG19 0.66
AGG20 0.50
FEAR21 0.82
FEAR23 0.81
FEAR24 0.86
FEAR25 0.43
FEAR26 0.44
FEAR27 0.85
FEAR28 0.66
FEAR29 0.50
FEAR30 0.64
FEAR31 0.70
SEPR32 0.68
SEPR33 0.60
SEPR34 0.74
EXCITE35 0.49
EXCITE36 0.61
EXCITE37 0.61
EXCITE38 0.63
PLAY43 0.56
PLAY44 0.81
PLAY45 0.76
PLAY46 0.71
IMP47 0.47
IMP48 0.45
MISC52 0.48
MISC53 0.50
MISC54 0.65
MISC55 0.72
MISC56 0.60
MISC59 0.52
MISC61 0.43
MISC62 0.42
MISC64 0.64
MISC65 0.64
MISC66 0.70
MISC67 0.61
MISC68 0.21

2.3.6.3 How many communalities < 0.40?

There are 1 items with communality < 0.40.

fanal13.communality item
MISC68 0.21 MISC68

2.3.6.4 13 Factor Model Loadings

PA2 PA1 PA12 PA4 PA13 PA9 PA7 PA8 PA5 PA6 PA3 PA11 PA10
TRAIN01 -0.10 -0.11 0.09 -0.03 0.03 -0.07 -0.04 0.00 0.02 0.00 0.64 0.09 -0.01
TRAIN03 -0.09 0.04 -0.02 -0.10 -0.07 0.06 0.09 0.07 0.12 -0.12 0.55 0.07 0.10
TRAIN04 -0.03 0.07 0.24 0.06 -0.07 0.01 0.02 0.01 -0.03 0.02 0.63 -0.06 0.00
TRAIN07 -0.12 0.04 0.59 0.02 -0.09 -0.04 0.00 0.02 0.00 0.03 0.30 0.01 -0.06
TRAIN08 -0.71 -0.01 0.11 0.02 -0.01 0.06 0.05 0.02 -0.10 0.08 0.08 0.00 0.02
AGG09 0.07 0.33 0.04 0.06 0.62 0.05 -0.06 -0.04 0.16 -0.06 0.07 -0.04 0.00
AGG10 0.07 0.00 0.00 0.07 0.73 -0.04 -0.02 0.10 0.13 0.01 -0.07 0.00 -0.01
AGG11 -0.08 -0.02 -0.16 0.77 -0.01 -0.02 -0.10 0.10 0.07 0.03 0.18 0.07 -0.01
AGG12 -0.08 0.07 0.05 0.88 -0.03 0.04 0.04 0.01 0.05 -0.01 -0.12 -0.07 0.03
AGG13 0.03 0.01 0.06 0.97 0.07 -0.01 0.04 -0.06 -0.02 0.01 0.00 0.04 0.00
AGG14 -0.03 0.03 0.07 -0.05 0.64 0.01 0.05 0.10 0.10 0.02 -0.06 -0.01 0.06
AGG15 -0.02 0.31 0.00 0.10 0.66 0.01 -0.02 -0.04 0.14 -0.11 0.01 0.06 0.01
AGG16 -0.05 -0.03 0.04 -0.03 0.19 0.07 -0.01 -0.06 0.73 0.20 0.04 -0.05 -0.03
AGG17 0.10 -0.02 0.05 0.20 0.41 0.09 0.12 0.13 -0.04 0.06 0.07 0.19 -0.46
AGG18 0.02 -0.08 0.00 -0.02 0.21 0.00 -0.04 -0.01 0.71 0.19 0.04 0.00 0.00
AGG19 0.05 -0.04 0.00 0.19 -0.01 0.02 0.11 0.04 0.69 -0.02 -0.01 0.12 -0.09
AGG20 -0.02 -0.07 -0.04 0.38 -0.10 0.03 0.00 0.04 0.49 -0.04 -0.03 0.16 0.06
FEAR21 -0.02 0.79 -0.02 0.05 0.10 0.03 0.01 0.01 -0.04 0.10 0.02 0.11 -0.03
FEAR23 -0.02 0.76 0.01 0.02 0.14 0.07 0.00 0.06 -0.02 0.15 -0.02 -0.04 -0.04
FEAR24 -0.10 0.80 0.00 0.06 0.12 -0.02 0.04 -0.01 -0.04 0.17 -0.03 0.04 -0.02
FEAR25 0.02 0.26 0.17 0.11 -0.07 0.32 0.03 0.04 -0.02 0.13 0.12 0.01 -0.03
FEAR26 0.05 0.35 -0.01 0.05 0.01 -0.02 0.00 0.05 0.01 0.09 0.01 0.42 0.02
FEAR27 0.02 0.16 0.01 0.03 -0.04 0.01 -0.01 0.02 0.13 0.83 -0.03 -0.01 0.00
FEAR28 0.03 0.48 0.11 0.00 -0.11 0.37 0.06 0.02 -0.02 0.05 0.02 0.20 -0.08
FEAR29 0.00 -0.01 0.00 -0.03 0.03 -0.04 0.01 0.02 -0.02 0.05 0.05 0.70 -0.01
FEAR30 0.05 0.02 0.05 0.02 -0.06 0.08 -0.03 0.06 0.07 -0.01 -0.03 0.73 0.05
FEAR31 0.00 0.09 0.03 -0.03 -0.10 0.04 0.01 0.02 0.05 0.75 0.00 0.08 0.04
SEPR32 -0.05 0.12 0.01 -0.06 -0.02 -0.05 0.08 0.78 0.08 -0.04 -0.08 0.07 -0.03
SEPR33 -0.02 -0.04 0.06 0.06 -0.04 0.01 0.00 0.76 -0.02 0.02 -0.04 0.01 0.05
SEPR34 -0.01 -0.10 -0.03 -0.01 0.10 0.06 -0.03 0.84 -0.10 0.06 0.10 0.00 -0.05
EXCITE35 -0.12 0.12 0.04 -0.11 0.00 -0.09 0.65 0.15 0.05 -0.02 -0.02 -0.02 0.06
EXCITE36 0.19 0.01 0.06 0.02 0.01 0.01 0.71 -0.05 -0.03 -0.07 -0.04 0.03 -0.04
EXCITE37 -0.08 -0.02 -0.02 0.02 0.01 -0.02 0.80 0.01 0.03 0.02 0.01 -0.02 0.00
EXCITE38 0.03 -0.04 -0.13 0.05 -0.03 0.07 0.77 -0.04 -0.01 0.04 0.06 0.01 -0.01
PLAY43 0.54 -0.30 0.03 0.00 -0.23 0.01 0.08 -0.04 -0.09 0.10 -0.08 -0.05 0.07
PLAY44 0.87 0.00 0.00 -0.02 -0.06 -0.03 0.05 -0.02 0.07 0.00 0.01 0.04 -0.06
PLAY45 0.84 -0.02 0.00 -0.08 0.08 -0.04 0.02 -0.05 -0.07 0.06 -0.09 0.01 0.02
PLAY46 0.76 -0.05 -0.16 0.00 0.12 0.02 0.03 0.03 -0.06 -0.05 0.06 -0.03 -0.07
IMP47 0.33 0.08 -0.02 0.03 0.02 0.03 0.14 0.07 0.03 0.05 0.36 0.00 0.35
IMP48 0.26 0.04 0.08 0.19 -0.02 0.04 0.12 0.11 0.05 0.03 0.21 -0.02 0.38
MISC52 -0.20 -0.19 0.02 0.01 0.24 0.05 0.10 -0.05 -0.17 0.17 0.01 0.18 0.50
MISC53 -0.13 -0.19 -0.04 0.17 0.08 -0.01 0.03 0.04 -0.13 0.06 0.11 0.14 0.55
MISC54 -0.08 -0.02 0.12 -0.06 0.01 0.69 0.05 -0.05 -0.01 0.01 0.00 0.15 0.02
MISC55 0.00 0.00 -0.06 -0.06 -0.01 0.87 0.00 0.05 0.06 -0.02 -0.04 -0.03 -0.03
MISC56 -0.01 -0.04 0.01 0.12 0.02 0.76 -0.04 -0.01 -0.04 0.03 0.01 -0.05 0.05
MISC59 0.29 0.15 0.15 0.04 -0.10 0.02 0.04 0.39 0.09 -0.12 0.10 -0.01 0.32
MISC61 0.39 0.11 0.07 -0.02 0.00 -0.09 0.22 0.23 0.07 -0.15 -0.04 -0.14 0.13
MISC62 0.01 -0.04 0.40 -0.05 0.02 -0.02 0.06 0.01 0.31 0.22 0.06 -0.01 0.11
MISC64 -0.03 -0.17 0.78 0.06 0.10 -0.01 -0.03 0.05 -0.06 0.04 0.02 0.02 -0.09
MISC65 -0.05 -0.11 0.68 -0.04 0.04 0.00 -0.01 0.03 0.09 0.06 0.13 0.07 0.04
MISC66 -0.05 0.24 0.60 -0.02 -0.03 0.20 -0.06 0.03 -0.03 -0.03 0.06 0.06 0.07
MISC67 -0.10 0.22 0.59 0.03 -0.02 0.15 -0.04 0.05 0.04 -0.02 -0.07 0.04 0.09
MISC68 0.11 -0.13 0.05 0.26 0.07 0.18 0.05 0.13 -0.08 0.14 0.15 -0.13 -0.13
2.3.6.4.1 13 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
17 PA1 0.79 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
18 PA1 0.76 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
19 PA1 0.80 FEAR24 When an unfamiliar person tries to touch or pet the dog
23 PA1 0.48 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
28 PA10 0.38 IMP48 Becomes frustrated/impatient in a wide range of situations
29 PA10 0.50 MISC52 Begs persistently for food when people are eating
30 PA10 0.55 MISC53 Steals food
21 PA11 0.42 FEAR26 When examined/treated by a veterinarian
24 PA11 0.70 FEAR29 When having nails trimmed, or feet touched/handled
25 PA11 0.73 FEAR30 When groomed or bathed
36 PA12 0.40 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
37 PA12 0.78 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
38 PA12 0.68 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
39 PA12 0.60 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
40 PA12 0.59 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
52 PA12 0.59 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
53 PA12 0.11 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
1 PA13 0.62 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA13 0.73 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA13 0.64 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA13 0.66 AGG15 When an unfamiliar person tries to touch or pet the dog
9 PA13 0.41 AGG17 When stared at directly by you or another familiar person
35 PA2 0.39 MISC61 Active, energetic, always on the go
42 PA2 0.54 PLAY43 Eagerly engages in play with new/unfamiliar people
43 PA2 0.87 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
44 PA2 0.84 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
45 PA2 0.76 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
27 PA3 0.36 IMP47 Impulsive; doesn’t seem to think before s/he acts
49 PA3 0.64 TRAIN01 Is hard to recall when off the leash
50 PA3 0.55 TRAIN03 Is slow to obey a ‘stay’ command
51 PA3 0.63 TRAIN04 Has difficulty attending/listening to things you say or do
3 PA4 0.77 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.88 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.97 AGG13 When his/her food is taken away by you or another familiar person
41 PA4 0.26 MISC68 Chases own tail/hind end
8 PA5 0.73 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA5 0.71 AGG18 When barked, growled, or lunged at by another dog
11 PA5 0.69 AGG19 Towards other familiar dogs
12 PA5 0.49 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
22 PA6 0.83 FEAR27 When approached directly by an unfamiliar dog
26 PA6 0.75 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
13 PA7 0.65 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
14 PA7 0.71 EXCITE36 Excitable when playing with you or other familiar persons
15 PA7 0.80 EXCITE37 Excitable just before being taken out for a walk
16 PA7 0.77 EXCITE38 Excitable just before being taken out for work or training
34 PA8 0.39 MISC59 Hyperactive, restless, has trouble settling down
46 PA8 0.78 SEPR32 Restlessness/agitation/pacing when left alone
47 PA8 0.76 SEPR33 Barking or whining when left alone
48 PA8 0.84 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
20 PA9 0.32 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
31 PA9 0.69 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
32 PA9 0.87 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
33 PA9 0.76 MISC56 Nervous or frightened when ascending or descending some types of stairs

2.3.7 13 Model Reliability Measures

2.4 14 Factors

2.4.1 Imputation of Missing Items (14 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.4.2 14-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.4.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum14, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1322 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 5.9267723^{4} with 1485 DF, p = 0e+00.

2.4.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8462795

2.4.3 14-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.4.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF14, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1321 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1485 DF, p = NaN.

2.4.3.2 14-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8462795

2.4.4 Between-Item Correlations

2.4.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.9.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.692. The maximum correlation was 0.903.

2.4.5 Estimating Number of Factors

2.4.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF14, n.obs = nrow(imputedNumericDF14), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 12.

2.4.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
Number of Factors MAP value
1 0.0314
2 0.0270
3 0.0212
4 0.0195
5 0.0186
6 0.0170
7 0.0167
8 0.0160
9 0.0154
10 0.0149
11 0.0150
12 0.0149
13 0.0153
14 0.0156
15 0.0161
16 0.0169
17 0.0169
18 0.0178

2.4.6 Factor Analysis for 14 Factors

2.4.6.1 14 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1321 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 5.1103584^{4}
  • degrees of freedom: 806
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.0848088. Should be > 0.9; need reference)

2.4.6.2 14 Factor Model Communalities

fanal14.communality
TRAIN01 0.60
TRAIN03 0.35
TRAIN04 0.54
TRAIN07 0.62
TRAIN08 0.64
AGG09 0.74
AGG10 0.68
AGG11 0.80
AGG12 0.83
AGG13 1.00
AGG14 0.51
AGG15 0.79
AGG16 0.77
AGG17 0.71
AGG18 0.74
AGG19 0.65
AGG20 0.54
FEAR21 0.82
FEAR23 0.81
FEAR24 0.86
FEAR25 0.44
FEAR26 0.44
FEAR27 0.85
FEAR28 0.66
FEAR29 0.54
FEAR30 0.65
FEAR31 0.69
SEPR32 0.68
SEPR33 0.60
SEPR34 0.77
EXCITE35 0.49
EXCITE36 0.61
EXCITE37 0.61
EXCITE38 0.64
PLAY43 0.56
PLAY44 0.81
PLAY45 0.76
PLAY46 0.71
IMP47 0.49
IMP48 0.46
MISC51 0.39
MISC52 0.47
MISC53 0.52
MISC54 0.65
MISC55 0.71
MISC56 0.64
MISC59 0.52
MISC60 0.61
MISC61 0.71
MISC62 0.45
MISC64 0.63
MISC65 0.64
MISC66 0.71
MISC67 0.60
MISC68 0.23

2.4.6.3 How many communalities < 0.40?

There are 3 items with communality < 0.40.

fanal14.communality item
TRAIN03 0.35 TRAIN03
MISC51 0.39 MISC51
MISC68 0.23 MISC68

2.4.6.4 14 Factor Model Loadings

PA2 PA1 PA3 PA4 PA5 PA9 PA8 PA13 PA7 PA6 PA12 PA10 PA11 PA14
TRAIN01 -0.09 -0.06 0.11 -0.05 -0.01 -0.05 -0.01 0.04 -0.03 -0.01 0.70 0.08 0.00 0.02
TRAIN03 -0.06 0.07 0.08 -0.09 -0.10 0.04 0.05 0.14 0.09 -0.14 0.44 0.08 0.02 0.14
TRAIN04 0.02 0.12 0.35 0.06 -0.11 0.00 0.02 0.00 0.03 -0.02 0.53 -0.06 -0.05 0.07
TRAIN07 -0.10 0.05 0.64 0.02 -0.10 -0.05 0.02 0.01 0.01 0.02 0.24 0.02 -0.02 -0.03
TRAIN08 -0.72 -0.01 0.10 0.03 -0.01 0.07 0.01 -0.11 0.05 0.08 0.09 0.02 0.00 -0.01
AGG09 0.04 0.31 0.04 0.07 0.63 0.06 -0.07 0.15 -0.08 -0.04 0.06 0.00 0.09 -0.03
AGG10 0.09 0.00 0.01 0.08 0.73 -0.05 0.10 0.14 -0.02 0.00 -0.08 0.00 -0.04 0.01
AGG11 -0.11 -0.01 -0.17 0.78 -0.03 0.00 0.08 0.08 -0.11 0.03 0.21 0.09 0.08 -0.04
AGG12 -0.04 0.07 0.08 0.88 -0.02 0.02 0.02 0.05 0.05 -0.01 -0.16 -0.07 -0.07 0.06
AGG13 0.02 0.00 0.05 0.96 0.08 -0.01 -0.07 -0.02 0.04 0.02 0.00 0.06 0.01 0.01
AGG14 0.02 0.04 0.08 -0.06 0.63 -0.01 0.12 0.11 0.06 0.00 -0.07 -0.04 -0.12 0.11
AGG15 -0.05 0.29 -0.02 0.10 0.67 0.02 -0.06 0.14 -0.03 -0.10 0.03 0.08 0.07 -0.01
AGG16 -0.04 -0.03 0.05 -0.04 0.19 0.06 -0.06 0.73 -0.01 0.20 0.02 -0.04 -0.01 -0.03
AGG17 0.18 0.01 0.05 0.19 0.39 0.09 0.18 -0.03 0.16 0.05 0.14 0.15 -0.25 -0.40
AGG18 0.01 -0.08 0.00 -0.03 0.21 0.00 -0.02 0.71 -0.04 0.19 0.04 0.01 0.04 -0.01
AGG19 0.05 -0.04 -0.04 0.17 0.00 0.03 0.05 0.69 0.11 -0.01 0.03 0.10 0.00 -0.09
AGG20 0.05 -0.05 -0.04 0.36 -0.12 0.02 0.08 0.52 0.02 -0.07 -0.03 0.11 -0.15 0.11
FEAR21 -0.02 0.79 -0.03 0.05 0.10 0.04 0.01 -0.04 0.01 0.09 0.02 0.10 0.02 -0.03
FEAR23 -0.02 0.76 0.02 0.02 0.14 0.06 0.07 -0.01 0.00 0.15 -0.03 -0.05 -0.01 -0.03
FEAR24 -0.11 0.79 -0.01 0.06 0.12 -0.02 -0.01 -0.05 0.04 0.17 -0.03 0.04 0.01 -0.03
FEAR25 0.06 0.30 0.20 0.10 -0.09 0.30 0.06 -0.01 0.04 0.10 0.09 -0.01 -0.09 0.02
FEAR26 0.03 0.34 -0.01 0.06 0.01 -0.02 0.03 0.01 0.00 0.09 0.00 0.44 0.03 0.01
FEAR27 0.02 0.16 0.00 0.03 -0.05 0.01 0.02 0.13 -0.01 0.82 -0.03 0.01 -0.02 0.01
FEAR28 0.06 0.50 0.14 0.00 -0.11 0.35 0.03 -0.01 0.07 0.03 -0.02 0.18 -0.08 -0.05
FEAR29 -0.03 -0.03 -0.02 -0.02 0.03 -0.03 -0.01 -0.04 0.00 0.05 0.05 0.74 0.05 -0.03
FEAR30 0.05 0.01 0.05 0.02 -0.06 0.07 0.06 0.06 -0.02 -0.02 -0.06 0.74 -0.05 0.06
FEAR31 0.01 0.11 0.04 -0.01 -0.11 0.04 0.02 0.06 0.01 0.73 -0.01 0.09 -0.05 0.05
SEPR32 -0.04 0.13 0.02 -0.06 -0.02 -0.06 0.78 0.09 0.08 -0.04 -0.11 0.07 0.01 -0.02
SEPR33 -0.02 -0.03 0.09 0.06 -0.05 -0.01 0.74 -0.01 0.00 0.01 -0.08 0.03 0.05 0.06
SEPR34 -0.01 -0.08 -0.04 -0.02 0.08 0.07 0.85 -0.09 -0.04 0.06 0.12 -0.01 0.03 -0.04
EXCITE35 -0.16 0.10 0.03 -0.11 0.01 -0.08 0.13 0.05 0.63 0.00 -0.03 -0.01 0.12 0.03
EXCITE36 0.15 -0.01 0.04 0.02 0.02 0.02 -0.06 -0.04 0.69 -0.05 -0.04 0.04 0.12 -0.06
EXCITE37 -0.08 -0.01 -0.02 0.01 0.01 -0.03 0.01 0.03 0.80 0.01 0.00 -0.03 0.01 0.01
EXCITE38 0.05 -0.02 -0.11 0.04 -0.05 0.06 -0.03 0.00 0.77 0.02 0.04 -0.01 -0.02 0.03
PLAY43 0.49 -0.31 0.02 0.00 -0.22 0.01 -0.05 -0.10 0.07 0.11 -0.09 -0.04 0.11 0.06
PLAY44 0.84 -0.01 0.00 -0.02 -0.05 -0.04 -0.02 0.07 0.05 0.00 0.01 0.03 0.07 -0.05
PLAY45 0.80 -0.03 -0.02 -0.08 0.08 -0.04 -0.06 -0.08 0.01 0.08 -0.09 0.01 0.11 0.01
PLAY46 0.76 -0.03 -0.15 0.00 0.11 0.01 0.04 -0.06 0.04 -0.05 0.08 -0.04 0.02 -0.04
IMP47 0.34 0.12 0.02 0.02 0.01 0.02 0.07 0.05 0.14 0.03 0.32 -0.02 0.04 0.40
IMP48 0.28 0.07 0.14 0.17 -0.03 0.02 0.11 0.07 0.12 0.01 0.13 -0.02 0.02 0.43
MISC51 -0.09 -0.10 0.00 0.02 0.08 0.03 0.28 0.03 0.05 0.00 0.40 -0.07 0.06 0.15
MISC52 -0.19 -0.18 0.00 0.01 0.23 0.05 -0.04 -0.16 0.09 0.17 0.02 0.16 -0.01 0.51
MISC53 -0.12 -0.17 -0.07 0.15 0.09 -0.01 0.06 -0.13 0.03 0.07 0.13 0.12 -0.01 0.57
MISC54 -0.05 0.00 0.13 -0.07 0.00 0.68 -0.03 0.00 0.07 0.00 -0.01 0.13 -0.11 0.05
MISC55 -0.01 0.00 -0.06 -0.07 -0.01 0.87 0.04 0.07 -0.01 -0.02 -0.05 -0.02 0.02 -0.03
MISC56 -0.06 -0.05 -0.01 0.12 0.02 0.79 -0.03 -0.04 -0.05 0.04 0.02 -0.02 0.08 0.02
MISC59 0.19 0.12 0.14 0.04 -0.08 0.03 0.34 0.08 0.00 -0.09 0.07 0.04 0.30 0.25
MISC60 0.06 -0.01 0.03 0.01 -0.03 0.06 0.01 -0.06 0.09 0.02 0.02 0.03 0.73 0.02
MISC61 0.14 0.04 -0.01 0.02 0.03 -0.04 0.12 0.05 0.13 -0.10 -0.04 -0.03 0.70 -0.05
MISC62 -0.06 -0.08 0.38 -0.04 0.03 0.00 -0.03 0.30 0.03 0.25 0.05 0.03 0.20 0.05
MISC64 -0.06 -0.19 0.75 0.07 0.11 0.00 0.05 -0.07 -0.03 0.05 0.02 0.03 0.04 -0.11
MISC65 -0.06 -0.12 0.69 -0.04 0.05 0.00 0.04 0.08 -0.01 0.07 0.11 0.07 0.01 0.04
MISC66 -0.03 0.24 0.63 -0.02 -0.01 0.19 0.05 -0.03 -0.06 -0.03 0.02 0.04 -0.03 0.09
MISC67 -0.11 0.20 0.58 0.03 0.00 0.14 0.06 0.03 -0.04 -0.01 -0.10 0.04 0.02 0.08
MISC68 0.07 -0.12 0.05 0.26 0.06 0.20 0.11 -0.08 0.04 0.14 0.17 -0.12 0.08 -0.13
2.4.6.4.1 14 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
17 PA1 0.79 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
18 PA1 0.76 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
19 PA1 0.79 FEAR24 When an unfamiliar person tries to touch or pet the dog
23 PA1 0.50 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
21 PA10 0.44 FEAR26 When examined/treated by a veterinarian
24 PA10 0.74 FEAR29 When having nails trimmed, or feet touched/handled
25 PA10 0.74 FEAR30 When groomed or bathed
36 PA11 0.73 MISC60 Playful, puppyish, boisterous
37 PA11 0.70 MISC61 Active, energetic, always on the go
29 PA12 0.40 MISC51 Escapes or would escape from home, yard or kennel given the chance
51 PA12 0.70 TRAIN01 Is hard to recall when off the leash
52 PA12 0.44 TRAIN03 Is slow to obey a ‘stay’ command
53 PA12 0.53 TRAIN04 Has difficulty attending/listening to things you say or do
8 PA13 0.73 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA13 0.71 AGG18 When barked, growled, or lunged at by another dog
11 PA13 0.69 AGG19 Towards other familiar dogs
12 PA13 0.52 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
27 PA14 0.40 IMP47 Impulsive; doesn’t seem to think before s/he acts
28 PA14 0.43 IMP48 Becomes frustrated/impatient in a wide range of situations
30 PA14 0.51 MISC52 Begs persistently for food when people are eating
31 PA14 0.57 MISC53 Steals food
44 PA2 0.49 PLAY43 Eagerly engages in play with new/unfamiliar people
45 PA2 0.84 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
46 PA2 0.80 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
47 PA2 0.76 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
38 PA3 0.38 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
39 PA3 0.75 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
40 PA3 0.69 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
41 PA3 0.63 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
42 PA3 0.58 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
54 PA3 0.64 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
55 PA3 0.10 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
3 PA4 0.78 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.88 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.96 AGG13 When his/her food is taken away by you or another familiar person
43 PA4 0.26 MISC68 Chases own tail/hind end
1 PA5 0.63 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA5 0.73 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA5 0.63 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA5 0.67 AGG15 When an unfamiliar person tries to touch or pet the dog
9 PA5 0.39 AGG17 When stared at directly by you or another familiar person
22 PA6 0.82 FEAR27 When approached directly by an unfamiliar dog
26 PA6 0.73 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
13 PA7 0.63 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
14 PA7 0.69 EXCITE36 Excitable when playing with you or other familiar persons
15 PA7 0.80 EXCITE37 Excitable just before being taken out for a walk
16 PA7 0.77 EXCITE38 Excitable just before being taken out for work or training
35 PA8 0.34 MISC59 Hyperactive, restless, has trouble settling down
48 PA8 0.78 SEPR32 Restlessness/agitation/pacing when left alone
49 PA8 0.74 SEPR33 Barking or whining when left alone
50 PA8 0.85 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
20 PA9 0.30 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
32 PA9 0.68 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
33 PA9 0.87 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
34 PA9 0.79 MISC56 Nervous or frightened when ascending or descending some types of stairs

2.4.7 14 Model Reliability Measures

2.5 15 Factors

2.5.1 Imputation of Missing Items (15 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.5.2 15-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.5.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum15, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1503 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1711 DF, p = NaN.

2.5.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8475668

2.5.3 15-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.5.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF15, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1502 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1711 DF, p = NaN.

2.5.3.2 15-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8475668

2.5.4 Between-Item Correlations

2.5.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.895.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.69. The maximum correlation was 0.897.

2.5.5 Estimating Number of Factors

2.5.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF15, n.obs = nrow(imputedNumericDF15), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 14.

2.5.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
Number of Factors MAP value
1 0.0286
2 0.0248
3 0.0194
4 0.0176
5 0.0168
6 0.0155
7 0.0150
8 0.0143
9 0.0142
10 0.0143
11 0.0140
12 0.0136
13 0.0138
14 0.0141
15 0.0146
16 0.0145
17 0.0150
18 0.0157

2.5.6 Factor Analysis for 15 Factors

2.5.6.1 15 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1502 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 5.1602564^{4}
  • degrees of freedom: 931
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.0677907. Should be > 0.9; need reference)

2.5.6.2 15 Factor Model Communalities

fanal15.communality
TRAIN01 0.54
TRAIN02 0.40
TRAIN03 0.57
TRAIN04 0.60
TRAIN07 0.62
TRAIN08 0.64
AGG09 0.75
AGG10 0.72
AGG11 0.75
AGG12 0.90
AGG13 0.98
AGG14 0.52
AGG15 0.77
AGG16 0.77
AGG17 0.79
AGG18 0.73
AGG19 0.73
AGG20 0.57
FEAR21 0.84
FEAR22 0.41
FEAR23 0.81
FEAR24 0.86
FEAR25 0.50
FEAR26 0.45
FEAR27 0.85
FEAR28 0.66
FEAR29 0.53
FEAR30 0.59
FEAR31 0.69
SEPR32 0.67
SEPR33 0.67
SEPR34 0.74
EXCITE35 0.50
EXCITE36 0.61
EXCITE37 0.60
EXCITE38 0.64
ATT39 0.29
ATT41 0.25
PLAY43 0.56
PLAY44 0.80
PLAY45 0.76
PLAY46 0.71
IMP47 0.48
IMP48 0.43
MISC51 0.50
MISC52 0.52
MISC53 0.53
MISC54 0.64
MISC55 0.74
MISC56 0.63
MISC59 0.50
MISC60 0.58
MISC61 0.68
MISC62 0.45
MISC64 0.63
MISC65 0.64
MISC66 0.68
MISC67 0.60
MISC69 0.22

2.5.6.3 How many communalities < 0.40?

There are 3 items with communality < 0.40.

fanal15.communality item
ATT39 0.29 ATT39
ATT41 0.25 ATT41
MISC69 0.22 MISC69

2.5.6.4 15 Factor Model Loadings

PA1 PA2 PA12 PA4 PA5 PA9 PA8 PA7 PA15 PA3 PA6 PA11 PA10 PA14 PA13
TRAIN01 -0.05 -0.10 0.16 -0.06 -0.04 -0.08 -0.03 -0.05 0.06 0.45 -0.02 0.11 0.06 0.03 0.35
TRAIN02 -0.05 -0.01 0.02 0.01 0.11 0.04 0.02 0.07 -0.09 0.61 0.04 -0.05 0.10 -0.05 -0.10
TRAIN03 -0.03 -0.07 -0.05 -0.06 0.04 0.05 0.07 0.07 0.07 0.73 -0.08 0.01 0.08 0.02 -0.08
TRAIN04 0.06 0.01 0.29 0.08 -0.06 -0.03 0.01 0.00 -0.06 0.58 0.04 0.00 -0.08 -0.04 0.14
TRAIN07 0.05 -0.10 0.64 0.02 -0.09 -0.07 0.02 0.00 0.01 0.23 0.01 -0.02 0.00 -0.03 0.02
TRAIN08 -0.02 -0.72 0.11 0.03 -0.02 0.07 0.01 0.06 -0.11 0.06 0.07 0.04 0.03 0.01 0.03
AGG09 0.29 0.03 0.04 0.09 0.66 0.07 -0.06 -0.07 0.08 0.05 -0.01 -0.03 -0.01 0.11 0.06
AGG10 -0.03 0.08 -0.02 0.10 0.79 -0.03 0.11 -0.01 0.06 0.00 0.01 0.00 0.03 -0.06 -0.04
AGG11 0.02 -0.12 -0.11 0.70 -0.06 -0.01 0.05 -0.10 0.15 0.03 -0.01 0.07 0.11 0.11 0.21
AGG12 0.02 -0.04 0.02 0.94 0.02 0.03 0.05 0.05 0.01 0.00 0.03 -0.03 -0.08 -0.06 -0.13
AGG13 0.00 0.01 0.05 0.94 0.08 -0.01 -0.06 0.04 0.00 -0.02 0.00 0.04 0.07 0.02 0.05
AGG14 0.09 0.04 0.08 -0.06 0.62 0.00 0.11 0.06 0.10 -0.06 -0.02 0.17 -0.07 -0.15 0.01
AGG15 0.30 -0.05 -0.03 0.11 0.65 0.03 -0.07 -0.04 0.11 0.04 -0.10 -0.01 0.08 0.07 0.09
AGG16 -0.08 -0.05 0.05 -0.02 0.28 0.07 -0.06 -0.02 0.62 0.07 0.29 -0.09 -0.06 0.02 -0.05
AGG17 0.06 0.14 0.13 0.14 0.29 0.09 0.14 0.19 0.03 -0.12 0.01 -0.24 0.17 -0.26 0.45
AGG18 -0.10 0.01 0.03 -0.03 0.28 0.00 -0.02 -0.05 0.63 0.02 0.26 -0.02 -0.02 0.06 0.00
AGG19 0.03 0.05 -0.01 0.10 -0.03 0.01 0.01 0.09 0.78 -0.02 -0.03 -0.06 0.09 0.00 0.07
AGG20 0.01 0.06 -0.01 0.31 -0.12 -0.01 0.05 -0.01 0.60 -0.03 -0.07 0.13 0.08 -0.14 -0.03
FEAR21 0.83 -0.02 -0.01 0.03 0.07 0.02 0.00 0.00 -0.01 -0.02 0.08 -0.01 0.08 0.03 0.05
FEAR22 0.35 -0.01 0.17 -0.06 -0.23 0.22 0.04 0.06 0.20 0.01 -0.10 0.08 0.06 -0.17 -0.16
FEAR23 0.77 -0.01 0.00 0.02 0.14 0.04 0.06 -0.01 -0.02 0.00 0.14 -0.05 -0.05 -0.01 -0.02
FEAR24 0.81 -0.11 -0.02 0.05 0.11 -0.04 -0.03 0.04 -0.03 -0.02 0.14 -0.03 0.06 0.02 -0.02
FEAR25 0.39 0.10 0.23 0.07 -0.15 0.27 0.05 0.03 0.10 0.03 0.02 0.11 -0.05 -0.14 -0.02
FEAR26 0.33 0.03 -0.01 0.05 0.01 -0.03 0.04 -0.01 0.02 0.04 0.10 0.02 0.44 0.04 -0.02
FEAR27 0.14 0.01 -0.02 0.04 -0.04 0.02 0.02 0.00 0.06 -0.02 0.85 0.01 0.01 -0.02 0.01
FEAR28 0.48 0.07 0.13 0.02 -0.10 0.34 0.04 0.06 -0.01 0.05 0.05 -0.08 0.17 -0.08 -0.05
FEAR29 -0.04 -0.02 0.01 -0.02 0.02 -0.01 0.02 0.00 0.00 0.05 0.06 0.05 0.70 0.04 0.03
FEAR30 0.00 0.06 0.04 0.05 -0.06 0.10 0.10 -0.04 0.07 0.04 0.04 0.08 0.65 -0.05 -0.04
FEAR31 0.09 -0.01 0.03 -0.02 -0.10 0.05 0.03 0.02 0.01 0.00 0.75 0.04 0.10 -0.05 -0.01
SEPR32 0.09 -0.04 0.00 -0.04 0.02 -0.06 0.78 0.07 0.06 -0.02 -0.01 -0.07 0.07 0.02 -0.06
SEPR33 -0.10 -0.02 0.03 0.10 0.02 0.01 0.80 -0.02 -0.06 0.07 0.05 -0.02 0.02 0.03 -0.14
SEPR34 -0.03 -0.02 0.00 -0.05 0.02 0.06 0.80 -0.03 -0.03 0.00 0.01 0.05 0.00 0.02 0.21
EXCITE35 0.10 -0.14 0.01 -0.10 0.02 -0.09 0.13 0.63 0.05 0.03 -0.01 0.03 -0.01 0.11 -0.07
EXCITE36 -0.01 0.15 0.03 0.04 0.01 0.01 -0.06 0.69 -0.04 0.01 -0.06 -0.06 0.06 0.10 -0.03
EXCITE37 -0.03 -0.08 -0.02 0.04 0.00 -0.02 0.01 0.78 0.01 0.02 0.04 0.02 -0.03 0.03 0.04
EXCITE38 -0.01 0.06 -0.11 0.05 -0.08 0.06 -0.03 0.77 0.02 0.03 0.02 0.06 -0.02 -0.04 0.05
ATT39 0.08 -0.07 0.10 -0.17 0.17 -0.08 0.08 0.21 0.03 -0.23 -0.03 0.10 0.08 0.16 -0.27
ATT41 0.05 0.05 0.15 0.03 -0.03 -0.03 0.15 0.09 0.07 -0.09 -0.03 0.30 -0.02 0.11 -0.21
PLAY43 -0.31 0.51 0.00 0.01 -0.22 0.02 -0.04 0.08 -0.09 -0.03 0.10 0.03 -0.04 0.08 -0.09
PLAY44 -0.03 0.83 0.00 -0.02 -0.03 -0.03 -0.02 0.05 0.07 0.02 0.01 -0.09 0.04 0.08 0.00
PLAY45 -0.02 0.81 -0.01 -0.08 0.08 -0.05 -0.06 0.02 -0.07 -0.07 0.05 0.00 0.03 0.08 -0.04
PLAY46 -0.02 0.75 -0.13 -0.02 0.08 0.01 0.03 0.04 -0.02 0.00 -0.08 -0.02 -0.04 0.00 0.10
IMP47 0.09 0.35 0.01 0.04 0.02 0.00 0.06 0.11 0.00 0.30 0.10 0.34 -0.06 0.09 0.10
IMP48 0.01 0.29 0.08 0.22 0.03 0.01 0.11 0.09 -0.01 0.25 0.09 0.29 -0.04 0.06 -0.08
MISC51 0.02 -0.08 0.08 -0.05 -0.06 0.00 0.22 0.03 0.14 0.09 -0.06 0.31 -0.11 0.09 0.43
MISC52 -0.06 -0.13 0.04 -0.03 0.14 0.03 -0.07 0.08 -0.06 -0.06 0.06 0.67 0.15 -0.05 -0.05
MISC53 -0.09 -0.08 -0.05 0.13 0.01 -0.02 0.03 0.00 -0.05 0.07 0.02 0.65 0.06 0.00 0.04
MISC54 0.00 -0.05 0.15 -0.05 0.00 0.67 -0.03 0.06 0.00 -0.01 0.01 0.08 0.12 -0.09 0.01
MISC55 0.00 -0.01 -0.08 -0.05 0.01 0.88 0.05 -0.01 0.06 0.02 -0.01 -0.04 -0.02 0.00 -0.04
MISC56 -0.07 -0.08 0.00 0.12 0.03 0.77 -0.04 -0.04 -0.08 0.00 0.07 0.01 0.02 0.12 0.08
MISC59 0.12 0.22 0.13 0.06 -0.10 0.03 0.32 -0.01 0.06 0.08 -0.04 0.18 -0.01 0.32 0.04
MISC60 0.00 0.10 0.05 0.00 -0.04 0.08 0.03 0.11 -0.07 0.01 -0.01 0.02 0.03 0.68 -0.04
MISC61 0.06 0.19 0.01 0.00 0.00 -0.01 0.13 0.16 0.05 -0.06 -0.12 -0.06 -0.04 0.64 0.01
MISC62 -0.08 -0.05 0.39 -0.04 0.04 0.01 -0.04 0.03 0.25 0.04 0.27 0.04 0.01 0.21 0.01
MISC64 -0.15 -0.06 0.79 0.05 0.07 -0.01 0.03 -0.02 -0.05 -0.04 0.01 -0.04 0.03 0.03 0.06
MISC65 -0.08 -0.05 0.71 -0.05 0.02 -0.01 0.02 -0.02 0.09 0.06 0.05 0.08 0.04 0.02 0.06
MISC66 0.24 -0.03 0.60 0.00 -0.01 0.16 0.05 -0.08 -0.04 0.09 -0.02 0.04 0.03 -0.02 -0.07
MISC67 0.22 -0.09 0.58 0.04 -0.01 0.13 0.05 -0.05 0.02 0.00 -0.01 0.03 0.03 0.01 -0.14
MISC69 0.07 0.01 0.12 0.04 -0.01 0.22 0.12 0.06 0.04 -0.05 0.10 0.14 -0.21 0.02 0.18
2.5.6.4.1 15 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
19 PA1 0.83 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
20 PA1 0.35 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
21 PA1 0.77 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
22 PA1 0.81 FEAR24 When an unfamiliar person tries to touch or pet the dog
23 PA1 0.39 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
26 PA1 0.48 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
24 PA10 0.44 FEAR26 When examined/treated by a veterinarian
27 PA10 0.70 FEAR29 When having nails trimmed, or feet touched/handled
28 PA10 0.65 FEAR30 When groomed or bathed
14 PA11 0.30 ATT41 Tends to nudge or paw you (or others) for attention
31 PA11 0.29 IMP48 Becomes frustrated/impatient in a wide range of situations
33 PA11 0.67 MISC52 Begs persistently for food when people are eating
34 PA11 0.65 MISC53 Steals food
41 PA12 0.39 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
42 PA12 0.79 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
43 PA12 0.71 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
44 PA12 0.60 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
45 PA12 0.58 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
58 PA12 0.64 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
59 PA12 0.11 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
9 PA13 0.45 AGG17 When stared at directly by you or another familiar person
32 PA13 0.43 MISC51 Escapes or would escape from home, yard or kennel given the chance
39 PA14 0.68 MISC60 Playful, puppyish, boisterous
40 PA14 0.64 MISC61 Active, energetic, always on the go
8 PA15 0.62 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA15 0.63 AGG18 When barked, growled, or lunged at by another dog
11 PA15 0.78 AGG19 Towards other familiar dogs
12 PA15 0.60 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
30 PA2 0.35 IMP47 Impulsive; doesn’t seem to think before s/he acts
47 PA2 0.51 PLAY43 Eagerly engages in play with new/unfamiliar people
48 PA2 0.83 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
49 PA2 0.81 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
50 PA2 0.75 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
54 PA3 0.45 TRAIN01 Is hard to recall when off the leash
55 PA3 0.61 TRAIN02 Is slow to obey a ‘sit’ command
56 PA3 0.73 TRAIN03 Is slow to obey a ‘stay’ command
57 PA3 0.58 TRAIN04 Has difficulty attending/listening to things you say or do
3 PA4 0.70 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.94 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.94 AGG13 When his/her food is taken away by you or another familiar person
1 PA5 0.66 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA5 0.79 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA5 0.62 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA5 0.65 AGG15 When an unfamiliar person tries to touch or pet the dog
25 PA6 0.85 FEAR27 When approached directly by an unfamiliar dog
29 PA6 0.75 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
13 PA7 0.21 ATT39 Displays a strong attachment for you or another familiar person
15 PA7 0.63 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
16 PA7 0.69 EXCITE36 Excitable when playing with you or other familiar persons
17 PA7 0.78 EXCITE37 Excitable just before being taken out for a walk
18 PA7 0.77 EXCITE38 Excitable just before being taken out for work or training
38 PA8 0.32 MISC59 Hyperactive, restless, has trouble settling down
51 PA8 0.78 SEPR32 Restlessness/agitation/pacing when left alone
52 PA8 0.80 SEPR33 Barking or whining when left alone
53 PA8 0.80 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
35 PA9 0.67 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
36 PA9 0.88 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
37 PA9 0.77 MISC56 Nervous or frightened when ascending or descending some types of stairs
46 PA9 0.22 MISC69 Chases/follows shadows, light spots, etc.

2.5.7 15 Model Reliability Measures

2.6 16 Factors

2.6.1 Imputation of Missing Items (16 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.6.2 16-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.6.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum16, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1647 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.6.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8510013

2.6.3 16-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.6.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF16, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1646 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.6.3.2 16-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8510013

2.6.4 Between-Item Correlations

2.6.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.892.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.69. The maximum correlation was 0.892.

2.6.5 Estimating Number of Factors

2.6.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF16, n.obs = nrow(imputedNumericDF16), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 14.

2.6.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
Number of Factors MAP value
1 0.0275
2 0.0237
3 0.0184
4 0.0167
5 0.0158
6 0.0147
7 0.0142
8 0.0134
9 0.0133
10 0.0131
11 0.0127
12 0.0126
13 0.0129
14 0.0130
15 0.0134
16 0.0137
17 0.0142
18 0.0147

2.6.6 Factor Analysis for 16 Factors

2.6.6.1 16 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1646 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 5.2319463^{4}
  • degrees of freedom: 1019
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.0665037. Should be > 0.9; need reference)

2.6.6.2 16 Factor Model Communalities

fanal16.communality
TRAIN01 0.56
TRAIN02 0.43
TRAIN03 0.63
TRAIN04 0.58
TRAIN07 0.62
TRAIN08 0.63
AGG09 0.76
AGG10 0.72
AGG11 0.82
AGG12 0.87
AGG13 0.98
AGG14 0.50
AGG15 0.78
AGG16 0.77
AGG17 0.73
AGG18 0.73
AGG19 0.72
AGG20 0.57
FEAR21 0.84
FEAR22 0.43
FEAR23 0.80
FEAR24 0.86
FEAR25 0.51
FEAR26 0.44
FEAR27 0.86
FEAR28 0.67
FEAR29 0.56
FEAR30 0.62
FEAR31 0.68
SEPR32 0.67
SEPR33 0.64
SEPR34 0.75
EXCITE35 0.50
EXCITE36 0.61
EXCITE37 0.61
EXCITE38 0.64
ATT39 0.30
ATT41 0.27
PLAY43 0.57
PLAY44 0.81
PLAY45 0.78
PLAY46 0.74
IMP47 0.59
IMP48 0.59
IMP49 0.39
MISC50 0.31
MISC51 0.54
MISC52 0.60
MISC53 0.51
MISC54 0.62
MISC55 0.74
MISC56 0.64
MISC59 0.56
MISC60 0.59
MISC61 0.66
MISC62 0.51
MISC63 0.37
MISC64 0.61
MISC65 0.63
MISC66 0.69
MISC67 0.60
MISC68 0.22

2.6.6.3 How many communalities < 0.40?

There are 6 items with communality < 0.40.

fanal16.communality item
ATT39 0.30 ATT39
ATT41 0.27 ATT41
IMP49 0.39 IMP49
MISC50 0.31 MISC50
MISC63 0.37 MISC63
MISC68 0.22 MISC68

2.6.6.4 16 Factor Model Loadings

PA9 PA1 PA2 PA4 PA3 PA7 PA5 PA8 PA6 PA10 PA13 PA12 PA16 PA14 PA11 PA15
TRAIN01 -0.03 0.18 -0.04 -0.05 -0.04 -0.07 -0.09 -0.04 0.06 0.45 -0.03 0.05 0.02 0.00 0.11 0.38
TRAIN02 -0.02 0.03 0.03 0.03 0.08 0.04 0.05 0.02 -0.10 0.63 0.06 0.04 0.00 -0.04 -0.01 -0.09
TRAIN03 0.00 -0.06 -0.02 -0.04 0.00 0.04 0.05 0.06 0.07 0.77 -0.07 0.03 0.03 0.04 0.03 -0.07
TRAIN04 0.04 0.29 -0.04 0.07 -0.05 0.00 -0.02 0.01 -0.08 0.49 0.04 -0.05 0.18 -0.05 -0.09 0.16
TRAIN07 0.05 0.63 -0.09 0.03 -0.09 -0.02 -0.07 0.04 -0.01 0.25 0.02 0.00 0.00 -0.03 -0.02 0.03
TRAIN08 0.00 0.10 -0.68 0.04 -0.02 0.05 0.07 0.02 -0.11 0.10 0.07 0.02 -0.10 0.01 0.07 0.03
AGG09 0.27 0.05 0.01 0.08 0.68 -0.07 0.07 -0.07 0.07 0.02 -0.02 0.00 0.05 0.11 -0.05 0.05
AGG10 -0.04 -0.02 0.08 0.09 0.79 -0.01 -0.02 0.12 0.07 0.01 0.02 0.02 0.00 -0.06 0.02 -0.07
AGG11 0.05 -0.11 -0.04 0.77 -0.07 -0.11 -0.01 0.07 0.14 0.08 0.01 0.07 -0.11 0.11 0.09 0.21
AGG12 0.02 0.03 -0.08 0.89 0.03 0.05 0.03 0.03 0.02 -0.03 0.02 -0.06 0.08 -0.07 -0.04 -0.16
AGG13 0.00 0.05 0.02 0.93 0.09 0.04 -0.01 -0.07 0.00 -0.01 0.00 0.08 0.02 0.00 0.02 0.01
AGG14 0.08 0.08 0.03 -0.05 0.62 0.05 -0.01 0.12 0.10 -0.04 -0.01 -0.06 0.02 -0.13 0.16 -0.01
AGG15 0.29 -0.03 -0.06 0.09 0.67 -0.03 0.03 -0.07 0.11 0.01 -0.10 0.10 0.01 0.05 -0.01 0.08
AGG16 -0.07 0.04 -0.05 -0.02 0.28 -0.02 0.06 -0.05 0.62 0.09 0.28 -0.05 -0.01 0.01 -0.07 -0.06
AGG17 0.07 0.14 0.16 0.15 0.33 0.19 0.08 0.16 0.02 -0.08 0.01 0.19 -0.15 -0.29 -0.20 0.34
AGG18 -0.10 0.02 0.00 -0.03 0.28 -0.05 -0.01 -0.01 0.63 0.02 0.24 0.00 0.03 0.05 -0.03 -0.01
AGG19 0.03 0.00 0.07 0.12 -0.02 0.10 0.02 0.02 0.76 -0.01 -0.01 0.08 -0.04 0.00 -0.05 0.09
AGG20 0.00 -0.03 0.03 0.30 -0.12 -0.01 -0.01 0.06 0.59 -0.04 -0.07 0.09 0.09 -0.15 0.08 -0.03
FEAR21 0.83 -0.02 -0.01 0.04 0.07 0.00 0.01 0.00 -0.01 -0.01 0.08 0.08 0.01 0.03 -0.02 0.04
FEAR22 0.38 0.17 0.03 -0.05 -0.25 0.04 0.21 0.04 0.20 0.05 -0.10 0.04 -0.04 -0.15 0.13 -0.15
FEAR23 0.76 0.01 -0.02 0.01 0.16 -0.01 0.05 0.05 -0.02 -0.02 0.15 -0.05 0.04 0.00 -0.06 -0.01
FEAR24 0.82 -0.02 -0.08 0.06 0.11 0.03 -0.04 -0.02 -0.04 0.00 0.16 0.03 -0.04 0.03 -0.01 -0.02
FEAR25 0.40 0.26 0.13 0.10 -0.15 0.02 0.28 0.04 0.07 0.06 0.04 -0.07 0.00 -0.12 0.13 0.00
FEAR26 0.33 -0.03 0.04 0.06 0.01 -0.01 -0.03 0.04 0.00 0.06 0.10 0.43 -0.01 0.03 0.03 -0.03
FEAR27 0.15 -0.01 0.02 0.04 -0.04 -0.01 0.02 0.03 0.07 -0.02 0.85 0.02 0.01 -0.02 0.02 0.01
FEAR28 0.49 0.13 0.05 -0.01 -0.10 0.06 0.33 0.02 0.00 0.04 0.02 0.18 0.02 -0.09 -0.06 -0.09
FEAR29 -0.05 -0.01 -0.04 -0.02 0.03 0.01 -0.03 0.00 -0.03 0.04 0.05 0.75 -0.02 0.05 0.04 0.01
FEAR30 -0.03 0.03 -0.01 0.03 -0.05 -0.02 0.08 0.07 0.05 -0.01 0.02 0.71 0.08 -0.04 0.03 -0.06
FEAR31 0.10 0.02 -0.02 -0.03 -0.11 0.01 0.05 0.03 0.02 -0.01 0.73 0.10 0.03 -0.06 0.05 -0.02
SEPR32 0.08 0.00 -0.07 -0.05 0.03 0.08 -0.05 0.77 0.07 -0.02 -0.01 0.08 0.04 0.01 -0.07 -0.07
SEPR33 -0.08 0.04 0.00 0.09 0.01 -0.02 0.01 0.76 -0.04 0.10 0.04 0.02 0.01 0.04 0.02 -0.14
SEPR34 -0.03 0.01 0.01 -0.03 0.03 -0.03 0.07 0.80 -0.04 0.01 0.03 0.00 0.01 0.01 0.05 0.21
EXCITE35 0.11 0.01 -0.11 -0.09 0.01 0.62 -0.08 0.15 0.04 0.07 0.00 -0.03 -0.04 0.13 0.06 -0.06
EXCITE36 -0.02 0.03 0.14 0.02 0.01 0.70 0.02 -0.05 -0.04 -0.01 -0.06 0.05 0.02 0.09 -0.06 -0.03
EXCITE37 -0.03 -0.02 -0.09 0.02 0.00 0.79 -0.03 0.01 0.02 0.01 0.03 -0.02 0.03 0.01 0.01 0.03
EXCITE38 -0.01 -0.10 0.04 0.03 -0.07 0.77 0.05 -0.04 0.03 0.01 0.01 -0.01 0.05 -0.04 0.04 0.04
ATT39 0.13 0.08 0.06 -0.09 0.12 0.17 -0.09 0.14 0.01 -0.06 0.01 -0.01 -0.23 0.20 0.22 -0.25
ATT41 0.07 0.13 0.10 0.07 -0.06 0.06 -0.04 0.17 0.06 0.00 -0.02 -0.05 -0.01 0.15 0.33 -0.20
PLAY43 -0.31 0.02 0.51 0.01 -0.23 0.07 0.03 -0.04 -0.09 -0.03 0.10 -0.05 0.02 0.09 0.03 -0.08
PLAY44 -0.02 0.01 0.84 -0.01 -0.04 0.04 -0.04 -0.02 0.07 0.02 0.01 0.04 0.05 0.06 -0.09 -0.01
PLAY45 0.01 0.00 0.85 -0.06 0.05 -0.01 -0.04 -0.04 -0.06 -0.04 0.06 -0.01 0.00 0.08 0.03 -0.05
PLAY46 0.01 -0.11 0.81 0.00 0.08 0.02 0.01 0.04 -0.01 0.04 -0.07 -0.06 -0.01 -0.02 0.00 0.08
IMP47 0.03 -0.06 0.14 -0.05 0.06 0.11 -0.01 0.01 -0.01 0.12 0.06 0.04 0.61 0.02 0.09 0.11
IMP48 -0.07 0.01 0.06 0.12 0.07 0.09 0.00 0.06 -0.01 0.07 0.05 0.05 0.63 0.00 0.06 -0.10
IMP49 0.00 0.10 0.03 0.18 0.01 0.12 -0.06 -0.07 -0.06 0.21 0.08 0.06 0.32 -0.04 0.07 0.14
MISC50 0.01 0.05 0.03 0.27 -0.06 0.09 0.05 0.23 -0.06 0.05 0.07 -0.09 0.16 0.11 -0.02 0.18
MISC51 0.00 0.08 -0.11 -0.06 -0.04 0.04 0.00 0.21 0.13 0.02 -0.06 -0.09 0.19 0.06 0.20 0.50
MISC52 -0.03 0.03 -0.04 0.00 0.12 0.04 0.03 -0.05 -0.06 0.00 0.06 0.07 0.00 -0.04 0.74 0.00
MISC53 -0.07 -0.06 -0.07 0.13 -0.01 -0.02 -0.03 0.03 -0.04 0.06 0.01 0.05 0.15 0.00 0.58 0.09
MISC54 0.02 0.14 -0.05 -0.06 -0.01 0.06 0.65 -0.03 0.00 0.01 0.00 0.12 0.01 -0.10 0.09 0.00
MISC55 0.00 -0.07 0.01 -0.05 0.01 -0.01 0.88 0.05 0.05 0.04 0.01 -0.02 -0.04 0.01 -0.02 -0.04
MISC56 -0.08 -0.02 -0.10 0.10 0.05 -0.03 0.78 -0.03 -0.06 -0.02 0.05 0.03 0.04 0.10 -0.01 0.07
MISC59 0.08 0.10 0.06 -0.01 -0.07 -0.01 0.01 0.30 0.06 -0.05 -0.09 0.07 0.43 0.28 -0.01 0.05
MISC60 0.01 0.05 0.13 0.02 -0.04 0.11 0.08 0.03 -0.08 0.03 -0.01 0.02 0.04 0.67 0.01 0.00
MISC61 0.08 0.00 0.22 0.00 0.01 0.16 -0.02 0.13 0.05 -0.02 -0.14 -0.03 0.04 0.60 -0.06 0.02
MISC62 -0.09 0.44 -0.07 -0.06 0.06 0.04 0.00 -0.08 0.26 -0.01 0.25 0.04 0.07 0.23 0.04 0.03
MISC63 -0.02 0.42 -0.02 0.04 0.02 0.15 0.09 -0.11 0.05 -0.04 0.07 0.00 0.12 0.16 0.13 0.04
MISC64 -0.13 0.77 -0.03 0.06 0.06 -0.04 -0.01 0.06 -0.05 0.01 0.01 0.03 -0.09 0.02 0.01 0.05
MISC65 -0.08 0.69 -0.07 -0.05 0.03 -0.03 -0.02 0.03 0.08 0.06 0.04 0.06 0.06 0.00 0.06 0.06
MISC66 0.22 0.59 -0.09 -0.02 0.00 -0.07 0.17 0.05 -0.05 0.04 -0.03 0.04 0.13 -0.03 0.00 -0.07
MISC67 0.23 0.54 -0.13 0.01 -0.01 -0.06 0.13 0.06 0.04 -0.02 -0.03 0.03 0.09 0.00 0.03 -0.13
MISC68 -0.09 0.09 0.08 0.25 0.03 0.06 0.19 0.11 -0.07 0.02 0.13 -0.09 -0.02 0.05 -0.06 0.21
2.6.6.4.1 16 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
43 PA1 0.44 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
44 PA1 0.42 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
45 PA1 0.77 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
46 PA1 0.69 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
47 PA1 0.59 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
48 PA1 0.54 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
61 PA1 0.63 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
57 PA10 0.45 TRAIN01 Is hard to recall when off the leash
58 PA10 0.63 TRAIN02 Is slow to obey a ‘sit’ command
59 PA10 0.77 TRAIN03 Is slow to obey a ‘stay’ command
60 PA10 0.49 TRAIN04 Has difficulty attending/listening to things you say or do
62 PA10 0.10 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
13 PA11 0.22 ATT39 Displays a strong attachment for you or another familiar person
14 PA11 0.33 ATT41 Tends to nudge or paw you (or others) for attention
35 PA11 0.74 MISC52 Begs persistently for food when people are eating
36 PA11 0.58 MISC53 Steals food
24 PA12 0.43 FEAR26 When examined/treated by a veterinarian
27 PA12 0.75 FEAR29 When having nails trimmed, or feet touched/handled
28 PA12 0.71 FEAR30 When groomed or bathed
25 PA13 0.85 FEAR27 When approached directly by an unfamiliar dog
29 PA13 0.73 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
41 PA14 0.67 MISC60 Playful, puppyish, boisterous
42 PA14 0.60 MISC61 Active, energetic, always on the go
9 PA15 0.34 AGG17 When stared at directly by you or another familiar person
34 PA15 0.50 MISC51 Escapes or would escape from home, yard or kennel given the chance
30 PA16 0.61 IMP47 Impulsive; doesn’t seem to think before s/he acts
31 PA16 0.63 IMP48 Becomes frustrated/impatient in a wide range of situations
32 PA16 0.32 IMP49 Is difficult to interrupt or distract when doing things s/he wants to do
40 PA16 0.43 MISC59 Hyperactive, restless, has trouble settling down
50 PA2 0.51 PLAY43 Eagerly engages in play with new/unfamiliar people
51 PA2 0.84 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
52 PA2 0.85 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
53 PA2 0.81 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.68 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.79 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.62 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.67 AGG15 When an unfamiliar person tries to touch or pet the dog
3 PA4 0.77 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.89 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.93 AGG13 When his/her food is taken away by you or another familiar person
33 PA4 0.27 MISC50 NA
49 PA4 0.25 MISC68 Chases own tail/hind end
37 PA5 0.65 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38 PA5 0.88 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
39 PA5 0.78 MISC56 Nervous or frightened when ascending or descending some types of stairs
8 PA6 0.62 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA6 0.63 AGG18 When barked, growled, or lunged at by another dog
11 PA6 0.76 AGG19 Towards other familiar dogs
12 PA6 0.59 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
15 PA7 0.62 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
16 PA7 0.70 EXCITE36 Excitable when playing with you or other familiar persons
17 PA7 0.79 EXCITE37 Excitable just before being taken out for a walk
18 PA7 0.77 EXCITE38 Excitable just before being taken out for work or training
54 PA8 0.77 SEPR32 Restlessness/agitation/pacing when left alone
55 PA8 0.76 SEPR33 Barking or whining when left alone
56 PA8 0.80 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
19 PA9 0.83 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
20 PA9 0.38 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
21 PA9 0.76 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
22 PA9 0.82 FEAR24 When an unfamiliar person tries to touch or pet the dog
23 PA9 0.40 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
26 PA9 0.49 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)

2.6.7 16 Model Reliability Measures

2.7 17 Factors

2.7.1 Imputation of Missing Items (17 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.7.2 17-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.7.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum17, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1639 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.7.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8528221

2.7.3 17-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.7.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF17, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1638 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.7.3.2 17-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8528221

2.7.4 Between-Item Correlations

2.7.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.892.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.69. The maximum correlation was 0.893.

2.7.5 Estimating Number of Factors

2.7.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF17, n.obs = nrow(imputedNumericDF17), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 15.

2.7.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
Number of Factors MAP value
1 0.0272
2 0.0236
3 0.0184
4 0.0167
5 0.0159
6 0.0148
7 0.0144
8 0.0135
9 0.0135
10 0.0132
11 0.0128
12 0.0127
13 0.0130
14 0.0132
15 0.0136
16 0.0139
17 0.0143
18 0.0147

2.7.6 Factor Analysis for 17 Factors

2.7.6.1 17 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1638 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 5.1792997^{4}
  • degrees of freedom: 973
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.1065804. Should be > 0.9; need reference)

2.7.6.2 17 Factor Model Communalities

fanal17.communality
TRAIN01 0.56
TRAIN02 0.44
TRAIN03 0.60
TRAIN04 0.58
TRAIN07 0.62
TRAIN08 0.63
AGG09 0.76
AGG10 0.71
AGG11 0.82
AGG12 0.87
AGG13 1.00
AGG14 0.50
AGG15 0.82
AGG16 0.77
AGG17 0.78
AGG18 0.74
AGG19 0.74
AGG20 0.57
FEAR21 0.83
FEAR22 0.43
FEAR23 0.80
FEAR24 0.86
FEAR25 0.51
FEAR26 0.44
FEAR27 0.87
FEAR28 0.67
FEAR29 0.54
FEAR30 0.68
FEAR31 0.68
SEPR32 0.67
SEPR33 0.68
SEPR34 0.75
EXCITE35 0.50
EXCITE36 0.61
EXCITE37 0.60
EXCITE38 0.64
ATT39 0.71
ATT40 0.42
ATT41 0.30
PLAY43 0.59
PLAY44 0.81
PLAY45 0.78
PLAY46 0.74
IMP47 0.61
IMP48 0.61
IMP49 0.39
MISC51 0.52
MISC52 0.57
MISC53 0.55
MISC54 0.63
MISC55 0.74
MISC56 0.66
MISC59 0.55
MISC60 0.60
MISC61 0.67
MISC62 0.52
MISC63 0.40
MISC64 0.60
MISC65 0.62
MISC66 0.70
MISC67 0.61
MISC68 0.22

2.7.6.3 How many communalities < 0.40?

There are 3 items with communality < 0.40.

fanal17.communality item
ATT41 0.30 ATT41
IMP49 0.39 IMP49
MISC68 0.22 MISC68

2.7.6.4 17 Factor Model Loadings

PA9 PA1 PA2 PA4 PA3 PA5 PA7 PA8 PA6 PA13 PA10 PA17 PA12 PA11 PA14 PA16 PA15
TRAIN01 -0.02 0.18 -0.06 -0.05 -0.06 -0.08 -0.07 -0.03 0.08 -0.03 0.42 0.07 0.02 0.14 0.02 -0.08 0.36
TRAIN02 -0.02 0.01 0.03 0.03 0.08 0.05 0.04 0.02 -0.09 0.06 0.65 0.00 0.05 -0.02 -0.03 0.01 -0.07
TRAIN03 -0.01 -0.04 -0.03 -0.05 0.01 0.05 0.04 0.06 0.08 -0.09 0.73 0.05 0.05 0.03 0.03 0.02 -0.07
TRAIN04 0.06 0.31 -0.04 0.06 -0.04 -0.03 0.01 0.03 -0.06 0.03 0.49 0.15 -0.06 -0.03 -0.02 -0.15 0.10
TRAIN07 0.05 0.61 -0.09 0.04 -0.10 -0.06 -0.03 0.04 -0.01 0.02 0.26 0.00 0.00 -0.03 -0.03 0.02 0.04
TRAIN08 -0.01 0.07 -0.69 0.05 -0.04 0.08 0.04 0.01 -0.11 0.07 0.11 -0.07 0.01 0.05 0.00 0.05 0.06
AGG09 0.23 0.05 0.00 0.08 0.67 0.07 -0.08 -0.08 0.06 -0.03 0.00 0.09 0.01 -0.07 0.07 0.09 0.08
AGG10 -0.06 -0.03 0.08 0.10 0.79 -0.02 -0.02 0.12 0.05 0.03 0.02 0.00 0.02 0.00 -0.07 0.05 -0.03
AGG11 0.05 -0.12 -0.06 0.76 -0.09 0.01 -0.12 0.06 0.16 0.00 0.07 -0.04 0.06 0.08 0.10 0.04 0.24
AGG12 0.03 0.04 -0.07 0.88 0.05 0.02 0.06 0.04 0.02 0.01 -0.03 0.04 -0.05 -0.02 -0.06 -0.05 -0.19
AGG13 0.00 0.05 0.01 0.94 0.08 0.00 0.04 -0.06 -0.01 0.01 -0.01 0.04 0.07 0.02 0.00 -0.01 0.03
AGG14 0.06 0.07 0.04 -0.05 0.62 -0.01 0.05 0.12 0.10 -0.01 -0.03 0.01 -0.05 0.15 -0.14 0.04 -0.01
AGG15 0.29 -0.01 -0.05 0.08 0.72 0.02 -0.01 -0.04 0.10 -0.09 0.01 -0.04 0.09 0.03 0.08 -0.10 0.04
AGG16 -0.09 0.04 -0.06 -0.02 0.27 0.06 -0.03 -0.07 0.60 0.28 0.08 0.04 -0.05 -0.11 -0.02 0.09 -0.03
AGG17 0.05 0.12 0.15 0.15 0.28 0.09 0.18 0.15 0.03 0.01 -0.08 -0.08 0.17 -0.21 -0.29 -0.03 0.44
AGG18 -0.12 0.01 -0.01 -0.03 0.26 0.01 -0.07 -0.04 0.62 0.24 0.02 0.10 0.00 -0.08 0.02 0.09 0.03
AGG19 0.04 0.02 0.08 0.12 0.01 0.00 0.12 0.03 0.77 0.00 0.00 -0.09 0.08 -0.01 0.03 -0.08 0.04
AGG20 0.00 -0.05 0.03 0.31 -0.13 0.00 -0.01 0.05 0.58 -0.07 -0.03 0.09 0.09 0.07 -0.15 0.01 -0.03
FEAR21 0.81 -0.03 -0.02 0.04 0.08 0.01 -0.01 0.00 -0.01 0.08 -0.01 0.02 0.08 -0.03 0.02 0.05 0.05
FEAR22 0.38 0.17 0.03 -0.05 -0.21 0.20 0.06 0.05 0.20 -0.09 0.06 -0.08 0.06 0.13 -0.15 0.00 -0.18
FEAR23 0.75 0.01 -0.02 0.01 0.18 0.04 0.00 0.06 -0.02 0.16 -0.02 0.02 -0.04 -0.05 0.01 -0.01 -0.03
FEAR24 0.79 -0.02 -0.09 0.07 0.12 -0.03 0.03 -0.02 -0.04 0.17 0.00 -0.02 0.03 -0.03 0.02 0.08 0.01
FEAR25 0.39 0.26 0.13 0.10 -0.14 0.28 0.02 0.04 0.08 0.04 0.05 0.01 -0.06 0.11 -0.13 0.02 -0.01
FEAR26 0.31 -0.05 0.03 0.07 0.01 -0.03 -0.02 0.03 -0.01 0.11 0.06 0.02 0.42 -0.01 0.03 0.06 0.03
FEAR27 0.16 0.00 0.02 0.03 -0.03 0.02 0.00 0.04 0.06 0.85 -0.02 0.00 0.02 0.03 -0.01 -0.02 0.00
FEAR28 0.48 0.12 0.04 0.00 -0.09 0.33 0.06 0.02 -0.01 0.03 0.03 0.03 0.19 -0.09 -0.09 0.01 -0.06
FEAR29 -0.06 -0.03 -0.04 -0.01 0.02 -0.03 0.00 -0.01 -0.04 0.05 0.05 0.00 0.73 0.03 0.04 0.04 0.07
FEAR30 -0.03 0.03 0.01 0.01 -0.01 0.05 -0.01 0.06 0.05 0.01 -0.01 0.02 0.77 0.06 -0.02 -0.07 -0.09
FEAR31 0.11 0.02 -0.02 -0.03 -0.12 0.06 0.01 0.03 0.02 0.73 0.00 0.05 0.10 0.04 -0.06 0.01 0.00
SEPR32 0.08 -0.01 -0.07 -0.05 0.02 -0.05 0.08 0.75 0.06 -0.01 -0.03 0.06 0.08 -0.09 0.00 0.07 -0.05
SEPR33 -0.08 0.03 0.01 0.09 0.02 0.00 -0.01 0.78 -0.05 0.06 0.10 -0.02 0.03 0.01 0.04 0.04 -0.14
SEPR34 -0.02 0.01 0.00 -0.04 0.03 0.07 -0.02 0.80 -0.03 0.02 0.00 0.02 0.00 0.07 0.03 -0.03 0.19
EXCITE35 0.10 0.01 -0.11 -0.09 0.02 -0.08 0.61 0.14 0.04 0.01 0.07 -0.04 -0.03 0.04 0.12 0.10 -0.05
EXCITE36 -0.02 0.03 0.13 0.03 0.01 0.02 0.69 -0.05 -0.04 -0.06 0.00 0.04 0.05 -0.07 0.09 0.05 0.00
EXCITE37 -0.03 -0.02 -0.09 0.02 0.00 -0.03 0.78 0.01 0.02 0.03 0.01 0.04 -0.02 0.01 0.02 0.02 0.03
EXCITE38 -0.01 -0.09 0.04 0.03 -0.06 0.05 0.77 -0.03 0.03 0.01 0.01 0.05 -0.01 0.05 -0.03 -0.01 0.02
ATT39 0.02 -0.01 0.05 -0.03 0.00 -0.02 0.06 0.01 0.00 -0.03 0.00 -0.06 -0.02 0.04 0.05 0.82 0.01
ATT40 0.03 0.23 -0.16 -0.02 -0.04 0.06 0.02 0.07 0.00 -0.03 -0.10 0.21 0.06 -0.01 -0.15 0.42 0.07
ATT41 0.02 0.09 0.08 0.09 -0.12 0.00 0.01 0.10 0.06 -0.04 0.00 0.11 -0.04 0.21 0.05 0.37 -0.09
PLAY43 -0.29 0.05 0.53 0.01 -0.20 0.02 0.09 -0.02 -0.09 0.11 -0.03 -0.05 -0.03 0.08 0.12 -0.08 -0.13
PLAY44 -0.02 0.01 0.83 -0.01 -0.05 -0.03 0.03 -0.03 0.08 0.01 0.02 0.07 0.04 -0.10 0.05 0.04 0.01
PLAY45 0.01 0.00 0.84 -0.06 0.05 -0.04 -0.01 -0.04 -0.06 0.06 -0.04 0.02 0.00 0.01 0.06 0.06 -0.02
PLAY46 0.01 -0.11 0.80 0.00 0.07 0.01 0.02 0.05 -0.01 -0.07 0.04 0.00 -0.07 0.00 -0.01 -0.02 0.09
IMP47 0.03 -0.07 0.13 -0.05 0.01 0.00 0.09 -0.01 -0.01 0.04 0.11 0.67 0.01 0.08 0.02 -0.03 0.09
IMP48 -0.07 -0.01 0.05 0.14 0.03 0.01 0.08 0.05 -0.03 0.04 0.05 0.67 0.03 0.02 -0.01 -0.01 -0.12
IMP49 0.00 0.09 0.03 0.18 -0.02 -0.05 0.11 -0.08 -0.05 0.06 0.21 0.35 0.05 0.07 -0.04 -0.02 0.13
MISC51 0.02 0.10 -0.11 -0.07 -0.03 0.00 0.05 0.23 0.15 -0.07 0.00 0.19 -0.11 0.27 0.08 -0.12 0.38
MISC52 -0.03 0.03 -0.05 0.00 0.14 0.03 0.04 -0.05 -0.07 0.08 0.00 0.00 0.09 0.71 -0.05 0.10 -0.01
MISC53 -0.05 -0.04 -0.04 0.12 0.03 -0.04 -0.01 0.05 -0.03 0.01 0.05 0.10 0.06 0.65 0.01 -0.02 0.01
MISC54 0.01 0.12 -0.05 -0.06 -0.03 0.66 0.04 -0.04 0.01 0.00 0.02 0.04 0.13 0.06 -0.11 0.05 0.03
MISC55 0.01 -0.06 0.02 -0.05 0.03 0.87 0.00 0.06 0.05 0.01 0.04 -0.06 -0.02 -0.01 0.01 -0.04 -0.06
MISC56 -0.08 -0.03 -0.10 0.11 0.02 0.80 -0.04 -0.04 -0.06 0.05 -0.02 0.06 0.01 -0.02 0.10 0.00 0.09
MISC59 0.08 0.10 0.06 -0.02 -0.07 0.01 0.00 0.30 0.07 -0.10 -0.07 0.42 0.08 0.00 0.28 -0.02 -0.01
MISC60 0.00 0.05 0.12 0.02 -0.03 0.08 0.10 0.04 -0.08 -0.01 0.03 0.04 0.02 0.00 0.67 0.07 -0.01
MISC61 0.08 0.01 0.20 0.00 0.02 -0.03 0.15 0.14 0.05 -0.13 -0.02 0.03 -0.03 -0.06 0.61 0.05 0.00
MISC62 -0.08 0.46 -0.07 -0.06 0.08 -0.01 0.05 -0.05 0.25 0.26 -0.02 0.05 0.04 0.06 0.23 -0.02 -0.02
MISC63 0.00 0.47 -0.01 0.02 0.08 0.06 0.17 -0.08 0.04 0.08 -0.06 0.06 0.02 0.19 0.17 -0.09 -0.06
MISC64 -0.13 0.74 -0.03 0.07 0.04 0.01 -0.05 0.06 -0.06 0.02 0.04 -0.07 0.03 -0.01 0.01 0.06 0.10
MISC65 -0.08 0.67 -0.07 -0.05 0.03 -0.02 -0.04 0.04 0.07 0.05 0.08 0.05 0.06 0.06 0.01 0.01 0.06
MISC66 0.21 0.59 -0.08 -0.02 0.01 0.16 -0.07 0.06 -0.05 -0.03 0.05 0.11 0.06 0.00 -0.04 0.00 -0.09
MISC67 0.21 0.54 -0.13 0.01 -0.01 0.13 -0.06 0.05 0.03 -0.04 -0.01 0.09 0.05 0.00 -0.03 0.08 -0.13
MISC68 -0.08 0.09 0.08 0.25 0.01 0.20 0.06 0.12 -0.06 0.12 0.03 -0.01 -0.11 -0.03 0.07 -0.05 0.21
2.7.6.4.1 17 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
43 PA1 0.46 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
44 PA1 0.47 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
45 PA1 0.74 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
46 PA1 0.67 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
47 PA1 0.59 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
48 PA1 0.54 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
61 PA1 0.61 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
57 PA10 0.42 TRAIN01 Is hard to recall when off the leash
58 PA10 0.65 TRAIN02 Is slow to obey a ‘sit’ command
59 PA10 0.73 TRAIN03 Is slow to obey a ‘stay’ command
60 PA10 0.49 TRAIN04 Has difficulty attending/listening to things you say or do
62 PA10 0.11 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
35 PA11 0.71 MISC52 Begs persistently for food when people are eating
36 PA11 0.65 MISC53 Steals food
25 PA12 0.42 FEAR26 When examined/treated by a veterinarian
28 PA12 0.73 FEAR29 When having nails trimmed, or feet touched/handled
29 PA12 0.77 FEAR30 When groomed or bathed
26 PA13 0.85 FEAR27 When approached directly by an unfamiliar dog
30 PA13 0.73 FEAR31 When barked, growled, or lunged at by an unfamiliar dog
41 PA14 0.67 MISC60 Playful, puppyish, boisterous
42 PA14 0.61 MISC61 Active, energetic, always on the go
9 PA15 0.44 AGG17 When stared at directly by you or another familiar person
34 PA15 0.38 MISC51 Escapes or would escape from home, yard or kennel given the chance
13 PA16 0.82 ATT39 Displays a strong attachment for you or another familiar person
14 PA16 0.42 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
15 PA16 0.37 ATT41 Tends to nudge or paw you (or others) for attention
31 PA17 0.67 IMP47 Impulsive; doesn’t seem to think before s/he acts
32 PA17 0.67 IMP48 Becomes frustrated/impatient in a wide range of situations
33 PA17 0.35 IMP49 Is difficult to interrupt or distract when doing things s/he wants to do
40 PA17 0.42 MISC59 Hyperactive, restless, has trouble settling down
50 PA2 0.53 PLAY43 Eagerly engages in play with new/unfamiliar people
51 PA2 0.83 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
52 PA2 0.84 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
53 PA2 0.80 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.67 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.79 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.62 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.72 AGG15 When an unfamiliar person tries to touch or pet the dog
3 PA4 0.76 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.88 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.94 AGG13 When his/her food is taken away by you or another familiar person
49 PA4 0.25 MISC68 Chases own tail/hind end
37 PA5 0.66 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38 PA5 0.87 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
39 PA5 0.80 MISC56 Nervous or frightened when ascending or descending some types of stairs
8 PA6 0.60 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA6 0.62 AGG18 When barked, growled, or lunged at by another dog
11 PA6 0.77 AGG19 Towards other familiar dogs
12 PA6 0.58 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
16 PA7 0.61 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
17 PA7 0.69 EXCITE36 Excitable when playing with you or other familiar persons
18 PA7 0.78 EXCITE37 Excitable just before being taken out for a walk
19 PA7 0.77 EXCITE38 Excitable just before being taken out for work or training
54 PA8 0.75 SEPR32 Restlessness/agitation/pacing when left alone
55 PA8 0.78 SEPR33 Barking or whining when left alone
56 PA8 0.80 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
20 PA9 0.81 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
21 PA9 0.38 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
22 PA9 0.75 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
23 PA9 0.79 FEAR24 When an unfamiliar person tries to touch or pet the dog
24 PA9 0.39 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
27 PA9 0.48 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)

2.7.7 17 Model Reliability Measures

2.8 18 Factors

2.8.1 Imputation of Missing Items (18 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.8.2 18-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.8.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

## Warning in polychoric(ddNum18, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1639 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.8.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8528221

2.8.3 18-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.8.3.1 Bartlett’s Test of Sphericity

## Warning in polychoric(imputedNumericDF18, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1638 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in log(detR): NaNs produced

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is NaN with 1891 DF, p = NaN.

2.8.3.2 18-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8528221

2.8.4 Between-Item Correlations

2.8.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.715. The maximum correlation in this data set is 0.892.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.69. The maximum correlation was 0.893.

2.8.5 Estimating Number of Factors

2.8.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

## Warning in fa.parallel(imputedNumericDF18, n.obs = nrow(imputedNumericDF18), :
## You specified the number of subjects, implying a correlation matrix, but do not
## have a correlation matrix, correlations found

The suggested number of factors is 15.

2.8.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in sqrt(e$values): NaNs produced
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected.  Examine the results carefully
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
## In smc, smcs > 1 were set to 1.0
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect.  Try a different factor score estimation method.
Number of Factors MAP value
1 0.0272
2 0.0236
3 0.0184
4 0.0167
5 0.0159
6 0.0148
7 0.0144
8 0.0135
9 0.0135
10 0.0132
11 0.0128
12 0.0127
13 0.0130
14 0.0132
15 0.0136
16 0.0139
17 0.0143
18 0.0147

2.8.6 Factor Analysis for 18 Factors

2.8.6.1 18 Factors Model Fit

## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1638 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

  • chi-square: 5.1334475^{4}
  • degrees of freedom: 928
  • P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: -0.1515229. Should be > 0.9; need reference)

2.8.6.2 18 Factor Model Communalities

fanal18.communality
TRAIN01 0.59
TRAIN02 0.44
TRAIN03 0.62
TRAIN04 0.58
TRAIN07 0.62
TRAIN08 0.64
AGG09 0.81
AGG10 0.71
AGG11 0.82
AGG12 0.88
AGG13 1.00
AGG14 0.51
AGG15 0.83
AGG16 0.77
AGG17 0.77
AGG18 0.73
AGG19 0.75
AGG20 0.64
FEAR21 0.83
FEAR22 0.43
FEAR23 0.80
FEAR24 0.86
FEAR25 0.54
FEAR26 0.45
FEAR27 0.87
FEAR28 0.67
FEAR29 0.53
FEAR30 0.69
FEAR31 0.67
SEPR32 0.67
SEPR33 0.68
SEPR34 0.76
EXCITE35 0.51
EXCITE36 0.61
EXCITE37 0.60
EXCITE38 0.65
ATT39 0.67
ATT40 0.47
ATT41 0.31
PLAY43 0.59
PLAY44 0.81
PLAY45 0.78
PLAY46 0.74
IMP47 0.62
IMP48 0.61
IMP49 0.39
MISC51 0.52
MISC52 0.59
MISC53 0.54
MISC54 0.63
MISC55 0.74
MISC56 0.66
MISC59 0.56
MISC60 0.59
MISC61 0.68
MISC62 0.58
MISC63 0.57
MISC64 0.68
MISC65 0.64
MISC66 0.69
MISC67 0.61
MISC68 0.23

2.8.6.3 How many communalities < 0.40?

There are 3 items with communality < 0.40.

fanal18.communality item
ATT41 0.31 ATT41
IMP49 0.39 IMP49
MISC68 0.23 MISC68

2.8.6.4 18 Factor Model Loadings

PA1 PA2 PA13 PA4 PA3 PA5 PA8 PA7 PA6 PA9 PA17 PA10 PA12 PA14 PA11 PA18 PA15 PA16
TRAIN01 -0.02 -0.05 0.12 -0.02 -0.07 -0.09 0.00 -0.07 0.03 -0.04 0.05 0.44 0.04 -0.02 0.10 0.12 -0.06 0.41
TRAIN02 -0.02 0.03 0.08 0.03 0.09 0.06 0.01 0.05 -0.09 0.06 0.01 0.62 0.05 -0.01 0.00 -0.10 -0.01 -0.08
TRAIN03 -0.02 -0.03 -0.05 -0.03 0.01 0.04 0.07 0.04 0.04 -0.09 0.04 0.75 0.05 0.02 0.02 0.01 0.03 -0.04
TRAIN04 0.06 -0.04 0.32 0.06 -0.04 -0.02 0.02 0.01 -0.06 0.03 0.17 0.47 -0.06 -0.02 -0.04 0.01 -0.15 0.09
TRAIN07 0.07 -0.09 0.60 0.02 -0.10 -0.05 0.02 -0.02 0.01 0.02 0.02 0.24 -0.01 -0.02 -0.03 0.06 0.01 0.01
TRAIN08 -0.01 -0.68 0.12 0.04 -0.04 0.09 0.00 0.05 -0.10 0.08 -0.07 0.09 0.01 0.01 0.06 -0.05 0.04 0.05
AGG09 0.22 0.01 -0.07 0.12 0.66 0.05 -0.04 -0.09 -0.01 -0.04 0.07 0.04 0.03 0.02 -0.12 0.20 0.12 0.12
AGG10 -0.06 0.08 0.00 0.09 0.79 -0.02 0.11 -0.02 0.04 0.04 0.00 0.01 0.01 -0.06 0.01 -0.03 0.05 -0.04
AGG11 0.04 -0.05 -0.09 0.76 -0.09 0.00 0.06 -0.12 0.15 0.00 -0.05 0.07 0.06 0.10 0.07 -0.05 0.04 0.25
AGG12 0.03 -0.07 0.00 0.89 0.04 0.02 0.05 0.06 0.02 0.01 0.04 -0.02 -0.04 -0.07 -0.03 0.06 -0.04 -0.19
AGG13 0.00 0.02 0.04 0.94 0.07 -0.01 -0.05 0.04 0.00 0.01 0.04 -0.01 0.07 0.00 0.02 0.01 -0.01 0.03
AGG14 0.07 0.04 0.09 -0.06 0.64 0.00 0.11 0.05 0.11 0.00 0.02 -0.04 -0.06 -0.13 0.16 -0.01 0.04 -0.02
AGG15 0.29 -0.06 0.04 0.06 0.73 0.03 -0.05 -0.01 0.11 -0.07 -0.02 -0.01 0.09 0.10 0.04 -0.03 -0.10 0.03
AGG16 -0.11 -0.05 -0.04 -0.01 0.27 0.06 -0.05 -0.04 0.52 0.29 0.02 0.11 -0.04 -0.04 -0.15 0.16 0.12 0.00
AGG17 0.05 0.16 0.18 0.15 0.29 0.09 0.14 0.20 0.04 0.02 -0.08 -0.10 0.17 -0.27 -0.20 -0.12 -0.04 0.39
AGG18 -0.14 -0.01 -0.06 -0.02 0.26 0.00 -0.02 -0.07 0.55 0.26 0.07 0.05 0.00 0.01 -0.11 0.14 0.12 0.06
AGG19 0.03 0.07 0.04 0.08 0.04 0.01 0.01 0.11 0.78 0.03 -0.07 0.00 0.07 0.05 -0.02 0.02 -0.08 0.04
AGG20 0.01 0.02 0.06 0.25 -0.10 0.02 0.00 -0.01 0.67 -0.04 0.13 -0.06 0.06 -0.10 0.10 -0.15 0.00 -0.06
FEAR21 0.81 -0.02 -0.01 0.04 0.08 0.01 -0.01 0.00 0.00 0.09 0.03 -0.01 0.08 0.03 -0.03 -0.03 0.04 0.05
FEAR22 0.38 0.03 0.10 -0.05 -0.21 0.19 0.06 0.05 0.21 -0.09 -0.09 0.07 0.06 -0.16 0.12 0.11 0.01 -0.16
FEAR23 0.75 -0.02 -0.02 0.02 0.17 0.04 0.06 -0.01 -0.03 0.16 0.01 -0.01 -0.04 0.00 -0.05 0.05 0.00 -0.03
FEAR24 0.79 -0.09 0.00 0.06 0.12 -0.03 -0.03 0.03 -0.03 0.17 -0.02 -0.01 0.03 0.03 -0.03 -0.04 0.07 0.00
FEAR25 0.40 0.14 0.11 0.13 -0.17 0.25 0.08 0.00 0.04 0.02 -0.02 0.08 -0.05 -0.18 0.08 0.23 0.05 0.03
FEAR26 0.32 0.03 0.03 0.05 0.02 -0.02 0.01 -0.01 0.02 0.12 0.03 0.04 0.41 0.06 0.02 -0.12 0.05 0.00
FEAR27 0.15 0.02 0.02 0.02 -0.03 0.03 0.03 0.00 0.05 0.86 0.01 -0.03 0.01 -0.01 0.03 0.01 -0.03 -0.01
FEAR28 0.48 0.05 0.04 0.01 -0.11 0.31 0.04 0.05 -0.02 0.02 0.01 0.05 0.20 -0.11 -0.10 0.10 0.03 -0.05
FEAR29 -0.06 -0.04 0.00 -0.01 0.02 -0.02 -0.01 0.01 -0.03 0.05 0.00 0.05 0.72 0.04 0.03 -0.04 0.04 0.06
FEAR30 -0.03 0.01 -0.02 0.02 -0.02 0.05 0.08 -0.02 0.04 0.00 0.02 0.01 0.78 -0.03 0.05 0.07 -0.06 -0.08
FEAR31 0.10 -0.02 0.02 -0.03 -0.12 0.06 0.03 0.01 0.00 0.73 0.05 0.00 0.10 -0.06 0.04 0.02 0.02 -0.01
SEPR32 0.07 -0.07 -0.02 -0.05 0.02 -0.06 0.75 0.08 0.06 -0.01 0.05 -0.03 0.09 0.01 -0.10 -0.01 0.07 -0.05
SEPR33 -0.07 0.01 0.03 0.10 0.02 0.00 0.79 -0.01 -0.05 0.05 -0.02 0.10 0.03 0.04 0.01 0.00 0.03 -0.15
SEPR34 -0.02 0.01 0.01 -0.03 0.03 0.06 0.82 -0.02 -0.03 0.02 0.02 0.00 0.00 0.02 0.05 0.00 -0.03 0.19
EXCITE35 0.10 -0.12 0.05 -0.10 0.03 -0.07 0.13 0.61 0.07 0.02 -0.02 0.06 -0.03 0.14 0.05 -0.04 0.09 -0.06
EXCITE36 -0.02 0.14 0.03 0.02 0.01 0.02 -0.06 0.68 -0.03 -0.06 0.05 -0.01 0.05 0.09 -0.06 0.00 0.05 -0.01
EXCITE37 -0.03 -0.09 -0.02 0.01 0.00 -0.02 0.01 0.77 0.03 0.03 0.05 0.01 -0.02 0.02 0.01 0.01 0.02 0.02
EXCITE38 -0.01 0.05 -0.14 0.05 -0.07 0.04 -0.01 0.76 0.02 0.00 0.04 0.02 0.00 -0.05 0.03 0.09 -0.01 0.04
ATT39 0.03 0.06 0.03 -0.04 0.01 -0.02 0.01 0.08 -0.01 -0.01 -0.08 -0.01 -0.03 0.09 0.06 -0.10 0.78 -0.02
ATT40 0.02 -0.14 0.10 0.01 -0.06 0.04 0.10 0.01 -0.07 -0.05 0.18 -0.08 0.08 -0.19 -0.06 0.17 0.48 0.11
ATT41 0.02 0.09 0.01 0.10 -0.13 -0.02 0.12 0.00 0.04 -0.04 0.08 0.03 -0.03 0.04 0.20 0.12 0.39 -0.07
PLAY43 -0.28 0.53 0.01 0.01 -0.21 0.01 -0.01 0.08 -0.09 0.09 -0.04 -0.02 -0.03 0.10 0.07 0.08 -0.08 -0.13
PLAY44 -0.02 0.83 0.01 -0.02 -0.05 -0.04 -0.03 0.04 0.07 0.01 0.07 0.02 0.04 0.06 -0.10 0.00 0.04 0.01
PLAY45 0.01 0.84 -0.01 -0.06 0.05 -0.04 -0.04 -0.01 -0.06 0.06 0.02 -0.04 0.00 0.07 0.01 0.01 0.05 -0.02
PLAY46 0.01 0.80 -0.08 0.00 0.08 0.01 0.04 0.03 0.00 -0.06 0.01 0.03 -0.07 0.01 0.01 -0.07 -0.03 0.08
IMP47 0.03 0.13 -0.03 -0.06 0.03 0.01 -0.02 0.10 0.01 0.05 0.67 0.09 0.01 0.03 0.08 -0.04 -0.03 0.09
IMP48 -0.07 0.05 0.01 0.13 0.04 0.02 0.04 0.08 -0.02 0.05 0.68 0.05 0.03 -0.01 0.03 0.00 0.00 -0.12
IMP49 0.00 0.03 0.12 0.17 -0.01 -0.05 -0.09 0.11 -0.04 0.06 0.35 0.20 0.05 -0.03 0.07 -0.02 -0.02 0.12
MISC51 0.01 -0.11 0.05 -0.06 -0.03 -0.01 0.25 0.04 0.13 -0.07 0.19 0.01 -0.10 0.06 0.23 0.12 -0.11 0.41
MISC52 -0.02 -0.05 0.03 -0.01 0.15 0.04 -0.05 0.04 -0.03 0.08 0.01 0.00 0.08 -0.04 0.72 0.03 0.10 0.00
MISC53 -0.06 -0.06 -0.05 0.12 0.03 -0.03 0.05 -0.01 -0.01 0.01 0.12 0.06 0.06 0.01 0.63 0.04 -0.01 0.03
MISC54 0.02 -0.05 0.09 -0.06 -0.03 0.65 -0.04 0.04 0.01 0.00 0.03 0.02 0.13 -0.12 0.06 0.04 0.06 0.03
MISC55 0.01 0.02 -0.04 -0.06 0.03 0.87 0.05 0.00 0.06 0.01 -0.05 0.04 -0.02 0.02 0.00 -0.02 -0.04 -0.07
MISC56 -0.08 -0.10 0.00 0.10 0.02 0.80 -0.04 -0.04 -0.06 0.05 0.07 -0.03 0.01 0.10 -0.01 -0.02 0.00 0.08
MISC59 0.08 0.05 0.10 -0.04 -0.07 0.02 0.28 -0.01 0.09 -0.10 0.44 -0.07 0.07 0.28 0.00 0.03 -0.02 -0.01
MISC60 0.01 0.12 0.03 0.01 -0.05 0.09 0.04 0.10 -0.08 -0.01 0.06 0.03 0.01 0.65 0.01 0.09 0.07 -0.01
MISC61 0.08 0.20 0.03 -0.01 0.02 -0.01 0.12 0.15 0.07 -0.12 0.05 -0.03 -0.05 0.62 -0.06 0.02 0.05 0.00
MISC62 -0.09 -0.06 0.21 -0.02 0.05 -0.05 0.00 0.02 0.15 0.24 0.01 0.03 0.06 0.16 -0.01 0.47 0.01 0.04
MISC63 -0.01 0.01 0.14 0.09 0.05 0.01 -0.01 0.14 -0.08 0.02 -0.01 -0.01 0.06 0.07 0.11 0.64 -0.06 0.01
MISC64 -0.11 -0.03 0.81 0.04 0.05 0.02 0.02 -0.04 -0.01 0.03 -0.05 -0.01 0.00 0.04 0.01 0.00 0.05 0.04
MISC65 -0.07 -0.07 0.65 -0.07 0.03 -0.01 0.02 -0.04 0.09 0.05 0.07 0.06 0.05 0.01 0.06 0.11 0.01 0.03
MISC66 0.23 -0.08 0.49 -0.03 0.00 0.16 0.06 -0.08 -0.05 -0.04 0.12 0.05 0.05 -0.06 -0.02 0.17 0.02 -0.09
MISC67 0.22 -0.14 0.47 -0.01 -0.02 0.13 0.04 -0.07 0.05 -0.04 0.10 -0.02 0.04 -0.03 -0.01 0.12 0.09 -0.14
MISC68 -0.08 0.08 0.17 0.23 0.02 0.21 0.10 0.06 -0.03 0.13 0.01 0.00 -0.12 0.09 -0.01 -0.09 -0.07 0.18
2.8.6.4.1 18 Factor Model Largest Loading Per Item
Largest Loading Per Item and Associated Factors, Sorted by Factor
largest maximum itemNames itemDescriptions
20 PA1 0.81 FEAR21 When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
21 PA1 0.38 FEAR22 In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
22 PA1 0.75 FEAR23 When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
23 PA1 0.79 FEAR24 When an unfamiliar person tries to touch or pet the dog
24 PA1 0.40 FEAR25 In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
27 PA1 0.48 FEAR28 When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
57 PA10 0.44 TRAIN01 Is hard to recall when off the leash
58 PA10 0.62 TRAIN02 Is slow to obey a ‘sit’ command
59 PA10 0.75 TRAIN03 Is slow to obey a ‘stay’ command
60 PA10 0.47 TRAIN04 Has difficulty attending/listening to things you say or do
35 PA11 0.72 MISC52 Begs persistently for food when people are eating
36 PA11 0.63 MISC53 Steals food
25 PA12 0.41 FEAR26 When examined/treated by a veterinarian
28 PA12 0.72 FEAR29 When having nails trimmed, or feet touched/handled
29 PA12 0.78 FEAR30 When groomed or bathed
45 PA13 0.81 MISC64 When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
46 PA13 0.65 MISC65 Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
47 PA13 0.49 MISC66 Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
48 PA13 0.47 MISC67 Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
61 PA13 0.60 TRAIN07 Unfocused; is easily distracted by interesting sights, sounds or smells
62 PA13 0.12 TRAIN08 Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
41 PA14 0.65 MISC60 Playful, puppyish, boisterous
42 PA14 0.62 MISC61 Active, energetic, always on the go
13 PA15 0.78 ATT39 Displays a strong attachment for you or another familiar person
14 PA15 0.48 ATT40 Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
15 PA15 0.39 ATT41 Tends to nudge or paw you (or others) for attention
9 PA16 0.39 AGG17 When stared at directly by you or another familiar person
34 PA16 0.41 MISC51 Escapes or would escape from home, yard or kennel given the chance
31 PA17 0.67 IMP47 Impulsive; doesn’t seem to think before s/he acts
32 PA17 0.68 IMP48 Becomes frustrated/impatient in a wide range of situations
33 PA17 0.35 IMP49 Is difficult to interrupt or distract when doing things s/he wants to do
40 PA17 0.44 MISC59 Hyperactive, restless, has trouble settling down
43 PA18 0.47 MISC62 Becomes highly excited and/or distracted when encountering unfamiliar dogs
44 PA18 0.64 MISC63 Becomes highly excited and/or distracted when encountering unfamiliar people
50 PA2 0.53 PLAY43 Eagerly engages in play with new/unfamiliar people
51 PA2 0.83 PLAY44 Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
52 PA2 0.84 PLAY45 Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
53 PA2 0.80 PLAY46 Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1 PA3 0.66 AGG09 Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2 PA3 0.79 AGG10 Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6 PA3 0.64 AGG14 When strangers walk past when the dog is in his/her home run or kennel
7 PA3 0.73 AGG15 When an unfamiliar person tries to touch or pet the dog
3 PA4 0.76 AGG11 Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4 PA4 0.89 AGG12 When you or another familiar person approaches the dog directly while s/he is eating
5 PA4 0.94 AGG13 When his/her food is taken away by you or another familiar person
49 PA4 0.23 MISC68 Chases own tail/hind end
37 PA5 0.65 MISC54 Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38 PA5 0.87 MISC55 Reluctant to/nervous about crossing shiny or slippery floors
39 PA5 0.80 MISC56 Nervous or frightened when ascending or descending some types of stairs
8 PA6 0.52 AGG16 When approached directly by an unfamiliar dog while being walked/exercised on a leash
10 PA6 0.55 AGG18 When barked, growled, or lunged at by another dog
11 PA6 0.78 AGG19 Towards other familiar dogs
12 PA6 0.67 AGG20 When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
16 PA7 0.61 EXCITE35 Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
17 PA7 0.68 EXCITE36 Excitable when playing with you or other familiar persons
18 PA7 0.77 EXCITE37 Excitable just before being taken out for a walk
19 PA7 0.76 EXCITE38 Excitable just before being taken out for work or training
54 PA8 0.75 SEPR32 Restlessness/agitation/pacing when left alone
55 PA8 0.79 SEPR33 Barking or whining when left alone
56 PA8 0.82 SEPR34 Chewing/scratching at doors, floor, fencing, etc., when left alone
26 PA9 0.86 FEAR27 When approached directly by an unfamiliar dog
30 PA9 0.73 FEAR31 When barked, growled, or lunged at by an unfamiliar dog

2.8.7 18 Model Reliability Measures